color

en-verb

color (third-person singular simple present colors, present participle coloring, simple past and past participle colored)

colors (present singular third-person)
coloring (participle present)
colored (participle past)
colored (past)
colour (alternative)
usage notes (alternative)

From Middle English colour, color, borrowed from Anglo-Norman colur, from Old French colour, color, from Latin color. Doublet of couleur.
Displaced English blee, Middle English blee (“color”), from Old English blēo. Also partially replaced Old English hīew (“color”) and its descendants (English hue), which is less often used in this sense.
The spelling color was popularized in modern American English by Noah Webster, to match the spelling of the word's Latin etymon, and make all American spellings of the derivatives consistent (colorimeter, coloration, colorize, colorless, etc).

Can this graph be 2-colored?

You can color any map with four colors.

(mathematics, graph theory) To assign colors to the vertices of a graph (or the regions of a map) so that no two vertices connected by an edge (regions sharing a border) have the same color.

färglägga

mathematics: assign distinct colors to the vertices or regions of


transitive

From Latin trānsitīvus, from trānsitus, from trāns (“across”) + itus, from eō (“to go”).

(graph theory, of a graph) Such that, for any two vertices there exists an automorphism which maps one to the other.


open

en-adj

open (comparative more open or (phonetics) opener, superlative most open or (phonetics) openest)

more open (comparative)
opener (comparative)
most open (superlative)
openest (superlative)

closed-source

antonym(s) of “with a free license and no proprietary components”

Adjective from Middle English open, from Old English open (“open”), from Proto-West Germanic *opan, from Proto-Germanic *upanaz (“open”), from Proto-Indo-European *upo (“up from under, over”).
Cognates
* Scots apen (“open”)
* Saterland Frisian eepen (“open”)
* West Frisian iepen (“open”)
* Dutch open (“open”)
* Low German open, apen (“open”)
* German offen (“open”)
* Danish åben (“open”)
* Swedish öppen (“open”)
* Norwegian Bokmål åpen (“open”)
* Norwegian Nynorsk open (“open”)
* Icelandic opinn (“open”)
 Compare also Latin supinus (“on one's back, supine”), Albanian hap (“to open”). Related to up.
Verb from Middle English openen, from Old English openian (“to open”), from Proto-West Germanic *opanōn, from Proto-Germanic *upanōną (“to raise; lift; open”), from Proto-Germanic *upanaz (“open”, adjective). Cognate with Saterland Frisian eepenje (“to open”), West Frisian iepenje (“to open”), Dutch openen (“to open”), German öffnen (“to open”), Danish åbne (“to open”), Swedish öppna (“to open”), Norwegian Bokmål åpne (“to open”), Norwegian Nynorsk and Icelandic opna (“to open”). Related to English up.
Noun from Middle English open (“an aperture or opening”), from the verb. In the sports sense, however, a shortening of “open competition”.

inh

at church every time the doors swing open

(graph theory, of a walk) Having different first and last vertices.


cherry

→ Bengali: চেরি (ceri)

→ Burmese: ချယ်ရီ (hkyairi)

→ Cantonese: 車厘子 /车厘子 (ce¹ lei⁴ zi²)

→ Hindi: चेरी (cerī)

→ Japanese: チェリー (cherī)

→ Kapampangan: tiéri

→ Korean: 체리 (cheri)

→ Malay: ceri

Indonesian: ceri

→ Maori: tiere

→ Punjabi: ਚੈਰੀ f (cairī)

→ Spanish: cherry

→ Swahili: cheri

→ Urdu: چیری (cerī)

→ Thai: เชอร์รี (chəə-rîi)

From Middle English chery, cherie, chirie, from Anglo-Norman cherise (mistaken as a plural) and Old English ċiris, ċirse (“cherry”), both ultimately from Vulgar Latin ceresia, derived from Late Latin ceresium, cerasium, from Ancient Greek κεράσιον (kerásion, “cherry fruit”), from κερασός (kerasós, “bird cherry”), and ultimately possibly of Anatolian origin (the intervocalic σ suggests a pre-Greek origin for the word). Doublet of cerise and kirsch.

dwarf cherry

P. fruticosa, P. pumila; Exocarpus strictus

Non-isomorphism is detected whenever the algorithm finds a cherry v#95;1#92;inT#95;1

2004, Suleyman Cenk Sahinalp, S Muthukrishnan, Ugur Dogrusoz, Combinatorial Pattern Matching, Berlin […] : Springer-Verlag, →ISBN, →ISSN, page 210:

Step 3: Output the tree T. The edge lengths of T are determined recursively: If (x,y) is a cherry connected to node z as in Step 2

2005, Lior Pachter, Bernd Sturmfels, Algebraic Statistics for Computational Biology, Cambridge, New York: Cambridge University Press, →ISBN, page 74:

(graph theory) A subtree consisting of a node with exactly two leaves.

kahdesta lehtisolmusta koostuva alipuu

graph theory: subtree consisting of two nodes


king

kings (plural)
kyng (alternative)
kynge (alternative)
kinge (alternative)

Tok Pisin: king

desc

⇒ American Sign Language: K@Shoulder K@Abdomen

→ Burmese: ကင် (kang)

→ Isubu: kinge

→ Japanese: キング (kingu)

→ Korean: 킹 (king)

→ Maori: kingi

→ Marshallese: kiin̄

→ Thai: คิง (king)

From Middle English king, kyng, from Old English cyng, cyning (“king”), from Proto-West Germanic *kuning, from Proto-Germanic *kuningaz, *kunungaz (“king”), equivalent to kin + -ing. Doublet of cyning and knez.
Cognate with Scots keeng (“king”), North Frisian köning (“king”), West Frisian kening (“king”), Dutch koning (“king”), Low German Koning, Köning (“king”), German König (“king”), Danish konge (“king”), Norwegian konge, Swedish konung, kung (“king”), Icelandic konungur, kóngur (“king”), Polish ksiądz (“priest”), Russian князь (knjazʹ, “prince”), Old Church Slavonic кънѧѕь (kŭnędzĭ), Romanian chinez, Finnish kuningas (“king”), Estonian kuningas, Ingrian kunigas, Karelian kuninkas, Livvi kuńingas, Ludian kuńingas, Veps kuningaz, Võro kuning and Votic kunikaz. Eclipsed non-native Middle English roy (“king”) (Early Modern English roy), borrowed from Old French roi, rei, rai (“king”).
The verb is inherited from Middle English kyngen, *kingen (“To perform the duties of a king”), itself from the noun king, kyng.

Audio — the king

акрал

a male of a royal family who is the supreme ruler of his nation

in the land of the blind, the one-eyed man is king

(graph theory) A vertex in a directed graph which can reach every other vertex via a path with a length of at most 2.


tree

Jamaican Creole: chrii

[t̠͡ɹ̠̊˔ʷiː]

From Middle English tre, tree, treo, treou, trew, trow, from Old English trēo, trēow (“tree, wood, timber, beam, log, stake, stick, grove, cross, rood”), from Proto-West Germanic *treu, from Proto-Germanic *trewą (“tree, wood”), from pre-Germanic *dréwom, thematic e-grade derivative of Proto-Indo-European *dóru (“tree”). Eclipsed alternative terms for tree in Middle English: Middle English beem, from Old English bēam (see beam) and Middle English arbre, from Old French arbre.
Cognates
From the same Proto-Indo-European: Scots tree (“wood, rod, stick”), North Frisian tre, trä (“tree”)Danish træ (“tree”), Swedish trä (“wood”), träd (“tree”), Norwegian tre (“tree”), Icelandic tré (“tree”), Gothic 𐍄𐍂𐌹𐌿 (triu, “tree, wood, piece of wood”), Sanskrit दारु (dāru, “tree, wood”), Albanian dru (“tree, wood”), Welsh dâr (“oaks”), Ancient Greek δόρυ (dóru, “wood, spear”), Russian де́рево (dérevo) or дре́во (drévo), Tocharian A or. Related to tar, true.

cog

fall out of the ugly tree and hit every branch

the apple does not fall far from the tree

the apple doesn't fall far from the tree

(graph theory) A connected graph with no cycles or, if the graph is finite, equivalently a connected graph with n vertices and n−1 edges.

ծառ

(graph theory) graph tree with no cycles


hole

→ Japanese: ホール (hōru)

→ Korean: 홀 (hol)

Sranan Tongo: olo

Inherited from Middle English hole, hol, from Old English hol (“orifice, hollow place, cavity”), from Proto-West Germanic *hol, from Proto-Germanic *hulą (“hollow space, cavity”), noun derivative of Proto-Germanic *hulaz (“hollow”), which is of uncertain ultimate origin. Related to hollow.

отвор

orifice (see anus etc. for specific body cavities)

know one's ass from a hole in the ground

know one's head from a hole in the ground

know the difference between one's ass and a hole in the ground

(graph theory) A chordless cycle in a graph.


rose

en-noun

rose (countable and uncountable, plural roses)

→ Marshallese: rooj

→ Tokelauan: loha

From Middle English rose, roose, from Old English rōse, but with its vowel influenced by Old French rose, both from Latin rosa. The Latin is of uncertain origin, but likely via Oscan from Ancient Greek ῥόδον (rhódon, “rose”) (Aeolic ϝρόδον (wródon)), from Old Persian *vr̥dah (“flower”) (compare Avestan 𐬬𐬀𐬭𐬆𐬜𐬀- (var^əδa-), Sogdian ward, Parthian wâr, late Middle Persian [Term?] (gwl /gul/), Persian گل (gol, “rose, flower”), and Middle Iranian borrowings including Old Armenian վարդ (vard, “rose”), Aramaic וַרְדָּא (wardā) / ܘܪܕܐ (wardā), Arabic وَرْدَة (warda), Hebrew וֶרֶד (wéreḏ)), from Proto-Indo-European *wr̥dʰos (“sweetbriar”) (compare Old English word (“thornbush”), Latin rubus (“bramble”), Albanian hurdhe (“ivy”)). Possibly ultimately a derivation from a verb for "to grow" only attested in Indo-Iranian (*Hwardʰ-, compare Sanskrit वर्धति (vardhati), with relatives in Avestan).

(mathematics, graph theory) A graph with only one vertex.


ear

Tok Pisin: ia

From Middle English ere, eare, from Old English ēare (“ear”), from Proto-West Germanic *auʀā, from the voiced Verner alternant of Proto-Germanic *ausô (“ear”) (compare Scots ear, West Frisian ear, Dutch oor, German Ohr, Swedish öra, Danish øre), from Proto-Indo-European *h₂ṓws (compare Old Irish áu, Latin auris, Lithuanian ausìs, Russian у́хо (úxo), Albanian vesh, Ancient Greek οὖς (oûs), Old Armenian ունկն (unkn), and Persian گوش (gôš)).

you can't make a silk purse of a sow's ear

(graph theory) A path whose endpoints may coincide but in which otherwise there are no repetitions of vertices or edges.


trail

→ German: Trail

→ Russian: трейл (trejl)

From Middle English trailen, from Old French trailler (“to tow; pick up the scent of a quarry”), from Vulgar Latin *tragulāre (“to drag”), from Latin tragula (“dragnet, javelin thrown by a strap”), probably related to Latin trahere (“to pull, drag along”).

der

(graph theory) A walk in which all the edges are distinct.


path

From Middle English path, peth, from Old English pæþ (“path, track”), from Proto-West Germanic *paþ, from Proto-Germanic *paþaz (“path”). The Proto-Germanic term is possibly borrowed from Iranian, from Proto-Iranian *pántaHh, from Proto-Indo-Iranian *pántaHs, from Proto-Indo-European *póntoh₁s, from the root *pent- (“to pass”), however this is disputed. Cognate with West Frisian paad, Dutch pad, German Pfad. Indo-Iranian cognates could be Avestan 𐬞𐬀𐬧𐬙𐬃 (paṇtā̊, “way”), Old Persian 𐎱𐎰 (p-θ /paθi/)), Sanskrit पन्था (panthā). See also English find). Doublet of panth.

(graph theory) A sequence of vertices from one vertex to another using the arcs (edges). A path does not visit the same vertex more than once (unless it is a closed path, where only the first and the last vertex are the same).

ruta

graph theory: a sequence of vertices from one vertex to another


cut

en-noun

cut (countable and uncountable, plural cuts)

From Middle English cutten, kitten, kytten, ketten (“to cut”) (compare Scots kut, kit (“to cut”)), of North Germanic origin, from Old Norse *kytja, *kutta, from Proto-Germanic *kutjaną, *kuttaną (“to cut”), of uncertain origin, perhaps related to Proto-Germanic *kwetwą (“meat, flesh”) (compare Old Norse kvett (“meat”)). Akin to Middle Swedish kotta (“to cut or carve with a knife”) (compare dialectal Swedish kåta, kuta (“to cut or chip with a knife”), Swedish kuta, kytti (“a knife”)), Norwegian Bokmål kutte (“to cut”), Norwegian Nynorsk kutte (“to cut”), Icelandic kuta (“to cut with a knife”), Old Norse kuti (“small knife”), Norwegian kyttel, kytel, kjutul (“pointed slip of wood used to strip bark”). Displaced native Middle English snithen (from Old English snīþan; compare German schneiden), which still survives in some dialects as snithe or snead. See snide. Adjective sense of "drunk" (now rare and now usually used in the originally jocular derivative form of half-cut) dates from the 17th century, from cut in the leg, to have cut your leg, euphemism for being very drunk.

leikkaus

notch, passage, or channel made by cutting or digging

(graph theory) The partition of a graph’s vertices into two subgroups.


card

en-noun

card (countable and uncountable, plural cards)

→ Bengali: কার্ড (karḍo)

→ Burmese: ကတ် (kat)

→ Chinese: 卡 (kǎ)

→ Gujarati: કાર્ડ (kārḍ)

→ Hausa: kati

→ Hindi: कार्ड (kārḍ)

→ Italian: card

→ Japanese: カード (kādo)

→ Korean: 카드 (kadeu)

→ Malay: kad

→ Pashto: کارډ (kārḍ)

Pitcairn-Norfolk: kaad

→ Sinhalese: කාඩ් (kāḍ)

→ Swahili: kadi

→ Tagalog: kard

→ Urdu: کارڈ (kārḍ)

From Middle English carde (“playing card”), from Old French carte, from Latin charta, from Ancient Greek χάρτης (khártēs, “paper, papyrus”). Doublet of chart.

der

Coordinate term: deck

(graph theory) A graph formed from a given graph by deleting one vertex.


bridge

bridges (plural)
bridg (alternative)
brigge (alternative)

From Middle English brigge, from Old English brycġ (“bridge”), from Proto-Germanic *brugjō, *brugjǭ (“bridge”), from Proto-Indo-European *bʰerw-, *bʰrēw- (“wooden flooring, decking, bridge”).
Cognate with Scots brig, brigg, breeg (“bridge”), Saterland Frisian Brääch (“bridge”), West Frisian brêge (“bridge”), Dutch brug (“bridge”), German Brücke (“bridge”), Danish brygge (“wharf”), Icelandic brygga (“pier”), Gaulish briua (“bridge”).
The verb is from Middle English briggen, from Old English brycġian (“to bridge, make a causeway, pave”), derived from the noun. Cognate with Dutch bruggen (“to bridge”), Middle Low German bruggen (“to bridge”), Old High German bruccōn (“to bridge”) (whence Modern German brücken).
The musical connection sense is a semantic loan from German Steg, from Old High German steg.

ацҳа

construction or natural feature that spans a divide

if someone told you to jump off a bridge, would you do it

(graph theory) An edge which, if removed, changes a connected graph to one that is not connected.


branch

From Middle English branche, braunche, bronche, from Old French branche, branke, from Late Latin branca (“footprint”, later also “paw, claw”) (whence Middle High German pranke, German Pranke (“paw”)), of unknown origin.
Perhaps of Celtic origin, from a hypothetical Gaulish *vranca, from Proto-Indo-European *wrónk-eh₂. If so, then Indo-European cognates include Old Norse rá, vró (“angle, corner”), and possibly Lithuanian rankà (“hand”), Old Church Slavonic рѫка (rǫka, “hand”), Albanian rangë (“yardwork”).
The verb is from Middle English braunchen, from the noun.

unk

unknown

the highest branch is not the safest roost

(graph theory) A path of vertices of degree 2, ending at vertices whose degree is not 2.


volume

en-noun

volume (countable and uncountable, plural volumes)

From Middle English volume, from Old French volume, from Latin volūmen (“book, roll”), from volvō (“roll, turn about”).

(graph theory) The sum of the degrees of a set of vertices.


cycle

→ Japanese: サイクル (saikuru)

From Middle English cicle (“fixed length period of years”), from Late Latin cyclus, from Ancient Greek κύκλος (kúklos, “circle”), from Proto-Hellenic *kúklos, *kʷókʷlos, from Proto-Indo-European *kʷékʷlos (“circle, wheel”).
Doublet of chakra, chakram, charkha, chukker, cyclus, and wheel (see there for more).

pyörä

bicycle, tricycle, motorcycle etc. — see also bicycle

(graph theory) A closed walk or path, with or without repeated vertices allowed.


size

en-noun

size (countable and uncountable, plural sizes)

→ Cantonese: size (saai1 si2)

→ Irish: saghas

→ Japanese: サイズ (saizu)

→ Korean: 사이즈 (saijeu)

→ Malay: saiz

→ Persian: سایز (sâyz)

→ Urdu: سائز (sāiz)

Attested since the 14th century, originally meant a “law or regulation that determines the amount to be paid”, from Middle English syse, sise (“regulation, control, limit”), from Old French cise, sise, aphetism of assise (“assize”), from the verb asseoir (“to sit down”), from Latin assidēre, composed of ad- (“to, towards, at”) + sedeō (“sit; settle down”), ultimately from Proto-Indo-European *sed-. Displaced native Old English miċelnes (literally “bigness”).

ncog

(graph theory) The number of edges in a graph.

koko

graph theory: a number of edges in a graph


tournament

→ Japanese: トーナメント (tōnamento)

Old French tornoiement (Modern French tournoiement) from the verb tornoier.

(graph theory) A digraph obtained by assigning a direction to each edge in an undirected complete graph.


order

en-noun

order (countable and uncountable, plural orders)

→ Swahili: oda

From Middle English ordre, from Old French ordre, ordne, ordene (“order, rank”), from Latin ōrdinem, accusative of ōrdō (“row, rank, regular arrangement”, literally “row of threads in a loom”), from Proto-Italic *ordō (“to arrange”), probably ultimately from Proto-Indo-European *h₂or-d-, from *h₂er-.
Related to Latin ōrdior (“begin”, literally “begin to weave”). In sense “request for purchase”, compare bespoke. Doublet of ordo.

cog

(graph theory, of a graph) The number of vertices in the graph (i.e. the set-theoretic order of the set of vertices of the graph).

řád

graph theory: number of vertices in a graph


line

→ Scottish Gaelic: loidhne

From Middle English line, lyne, from Old English līne (“line, cable, rope, hawser, series, row, rule, direction”), from Proto-West Germanic *līnā, from Proto-Germanic *līnǭ (“line, rope, flaxen cord, thread”), from Proto-Germanic *līną (“flax, linen”), from Proto-Indo-European *līno- (“flax”).
Influenced in Middle English by Middle French ligne (“line”), from Latin linea. More at linen.
The oldest sense of the word is “rope, cord, thread”; from this the senses “path”, “continuous mark” were derived.

lyn

path through two or more points, threadlike mark

lyn

single horizontal row of text on a screen, printed paper, etc.

linja

measure of length, the main division of an inch or its local equivalent

A path through two or more points (compare ‘segment’); a continuous mark, including as made by a pen; any path, curved or straight.


graph

Clipping of graphic formula. From 1878; verb from 1889.

1973, Edward Minieka (translator), Claude Berge, Graphs and Hypergraphs, Elsevier (North-Holland), [1970, Claude Berge, Graphes et Hypergraphes], page vii,
Problems involving graphs first appeared in the mathematical folklore as puzzles (e.g. Königsberg bridge problem). Later, graphs appeared in electrical engineering (Kirchhof's Law), chemistry, psychology and economics before becoming a unified field of study.

Spectral graph theory has a long history. In the early days, matrix theory and linear algebra were used to analyze adjacency matrices of graphs. Algebraic methods are especially effective in treating graphs which are regular and symmetric.

1997, Fan R. K. Chung, Spectral Graph Theory, American Mathematical Society, page 1:

Graph (discrete mathematics)
w:Graph (discrete mathematics)

(graph theory) A set of vertices (or nodes) connected together by edges; (formally) an ordered pair of sets (V,E), where the elements of V are called vertices or nodes and E is a set of pairs (called edges) of elements of V. See also Graph (discrete mathematics) on Wikipedia.Wikipedia


genus

en-noun

genus (plural genera or (all nonstandard) genuses or genusses or genii)

genera (plural)
genuses (nonstandard plural)
genusses (nonstandard plural)
genii (nonstandard plural)

→ Malayalam: ജീനസ് (jīnasŭ)

→ Swahili: jenasi

→ Thai: สกุล (sà-gun) (semantic loan)

Etymology tree
Proto-Indo-European *ǵenh₁-
Proto-Indo-European *-os
Proto-Indo-European *ǵénh₁os
Latin genusbor.
English genus
Borrowed from Latin genus (“birth, origin, a race, sort, kind”) from the root gen- in Latin gignō (“to beget, produce”). Doublet of gender, genre, and kin.

genus

rank in a taxonomic classification between family and species

(topology, graph theory, algebraic geometry) A natural number representing any of several related measures of the complexity of a given manifold or graph.


dag

Abbreviations
* Initialism of directed acyclic graph.
* Clipping of dagwood.

partial ordering relation
partial ordering relation

(graph theory) A directed acyclic graph; an ordered pair (V,E) such that E is a subset of some partial ordering relation on V.


circuit

From Middle English circuit, from Old French circuit, from Latin circuitus (“a going round”), from circuire (“go round”), from circum (“around”) + ire. As a Chinese administrative division, a calque of Chinese 道 (dào) or 路 (lù).

piiri

Methodist Church: district in which an itinerant preacher labors

dao

Imperial Chinese administrative divisions

(graph theory) A closed path, without repeated vertices allowed.


degree

From Middle English degre, borrowed from Old French degré (French: degré), itself from Latin gradus, with the prefix de-.

Appendix:Roget MICRA thesaurus/Class I § 26. Degree

Appendix:Roget MICRA thesaurus/Class I § 31. Greatness

Appendix:Roget MICRA thesaurus/Class I § 32. Smallness

(graph theory) The number of edges that a vertex takes part in; a valency.

次數 /次数

graph theory: the number of edges that a vertex takes part in


arrow

From Middle English arwe, from Old English earh (oblique form ēarw-), from Proto-West Germanic *arhu, from Proto-Germanic *arhwō, from Proto-Indo-European *h₂érkʷo- (“bow, arrow”). Cognate with Faroese ørv (“arrow”), Icelandic ör (“arrow”), örvar (“arrows”), Gothic 𐌰𐍂𐍈𐌰𐌶𐌽𐌰 (arƕazna, “dart”), Latin arcus (“bow”).


forest

en-noun

forest (countable and uncountable, plural forests)

forced (US, sometimes especially in fast speech)

From Middle English forest, from Old French forest, from Early Medieval Latin forestis, likely from Frankish or Proto-West Germanic *furhisti (“forest, fir-grove, wooded land”); related to Old English fyrhþe (“forested land”), Old High German forst, forsti (“forest”), Old Norse fýri (“pine forest”). Doublet of frith.
In this sense, mostly displaced the native Middle English wode, from Old English wudu (modern English wood) and Middle English wold, wald, wæld, from Old English weald (modern English wold, weald).

der

Let H be a traversal of an undirected graph G = (X, U). For given H, the set U can be split into set of tree edges from the forest G_H and the set of inverse edges that do not belong to this forest.

2000, Victor N. Kasyanov, Vladimir A. Evstigneev, Graph Theory for Programmers: Algorithms for Processing Trees, Springer Science & Business Media, →ISBN, page 16:

(graph theory) A graph with no cycles; i.e., a graph made up of trees.


closed

(graph theory, of a walk) Whose first and last vertices are the same, forming a closed loop.


crossing

en-noun

crossing (countable and uncountable, plural crossings)

(graph theory) A pair of intersecting edges.


tie

From Middle English teye (“cord, chain”), from Old English tēag, tēah (“cord, chain”), from Proto-West Germanic *taugu, from Proto-Germanic *taugō, ultimately from Proto-Indo-European *dewk-. Compare Danish tov, Icelandic taug.

(graph theory) A connection between two vertices.


radius

Borrowed from Latin radius (“ray”). Doublet of ray.

(graph theory) The minimum eccentricity of any vertex, for a given graph.


arc

→ Irish: arc

→ Maltese: ark

→ Welsh: arc

Inherited from Middle English ark, from Old French arc, from Latin arcus (“a bow, arc, arch”), ultimately from Proto-Indo-European *h₂erkʷos (“bow, arrow”). Doublet of arch, arco, and arrow.


minor

en-adj

minor (comparative more minor, superlative most minor)

more minor (comparative)
most minor (superlative)
miner (alternative)
maner (alternative)
minore (alternative)
minour (alternative)
mynor (alternative)
mynour (alternative)
mynowr (alternative)
mi (alternative)

antonym(s) of

serious, grave, severe, dangerous, fatal, life-threatening, acute (informal)

From Middle English minor, menor, menour, etc., from Latin minor (“lesser; young; young person”) both directly and via Norman and Middle French menor, menour, etc. Doublet of minus but not mini-. Cognate with minister, minify, Minorca, Menshevik, and possibly minnow. Compare Latin minimum and minuō, Old High German minniro, Cornish minow.

der

Lesser, smaller in importance, size, degree, seriousness, or significance compared to another option, particularly:

(graph theory) Including both directed and undirected edges.


spanner

Japanese: スパナ (supana)

Korean: 스패너 (seupaeneo)

Malay: sepana

(graph theory) A (usually sparse) graph whose shortest path distances approximate those in a dense graph or other metric space.


root

en-noun

root (countable and uncountable, plural roots)

→ Irish: rúta

From Middle English rote, root, roote (“the underground part of a plant”), from late Old English rōt, from Old Norse rót (Icelandic rót), from Proto-Germanic *wrōts, from Proto-Indo-European *wréh₂ds (“root”); Doublet of wort, radish, and radix.

the love of money is the root of all evil

(graph theory, computing) The single node of a tree that has no parent.

rod

graph theory: node in a tree that has no parent


walk

From Middle English walk, walke, walc, from Old English *wealc (as in Old English wealcspinl) and ġewealc (“a rolling motion, attack”), from Proto-Germanic *walką. Cognate with Icelandic válk (“a rolling around, a tossing to and fro, trouble, distress”).

cog

(graph theory) A sequence of alternating vertices and edges, where each edge's endpoints are the preceding and following vertices in the sequence. Compare path, trail.

kulku

graph theory: a sequence of alternating vertices and edges


source

non-rhotic, without the horse–hoarse merger

From Middle English sours, from Old French sorse (“rise, beginning, spring, source”), from sors, past participle of sordre, sourdre, from Latin surgō (“to rise”), which is composed of sub- (“up from below”) + regō (“lead, rule”), ultimately from Proto-Indo-European *h₃réǵeti (“to straighten; right”), from the root *h₃reǵ-. See surge.

der

(graph theory) A node in a directed graph whose edges all go out from it; one with no entering edges.


chord

Variant of cord, with spelling alteration due to Latin chorda (“cord”), ultimately from Ancient Greek χορδή (khordḗ, “string of gut, the string of a lyre”). No relation to French accord (“chord”) and its derivations.

(graph theory) An edge that is not part of a cycle but connects two vertices of the cycle.


breadth

en-noun

breadth (countable and uncountable, plural breadths)

From Middle English bredthe, alteration (due to nouns ending in -th: length, strength, wrength, etc.) of brede ("breadth"; see bread). Equivalent to broad + -th. Cognate with Scots bredth (“breadth”), Saterland Frisian Bratte (“breadth”), West Frisian breedte (“breadth”), Dutch breedte (“breadth”), German Low German Breddte, Breddt (“breadth”), German Breite (“breadth”), Danish bredde (“breadth”), Norwegian Bokmål bredde (“breadth”), Swedish bredd (“breadth”).

(graph theory) The length of the longest path between two vertices in a graph.


vertex

Late Middle English, borrowed from Latin vertex (“whirl, eddy; top, crown, peak, summit”). Doublet of vortex.

der

Mathworld article on vertices of polyhedra

Mathworld article on vertices of polygons

Coordinate term: plot

(graph theory) One of the elements of a graph joined or not by edges to other vertices.


edge

From Middle English egge, from Old English eċġ, from Proto-West Germanic *aggju, from Proto-Germanic *agjō, from Proto-Indo-European *h₂eḱ- (“sharp”).
See also Dutch egge, German Ecke, Swedish egg, Norwegian egg; also Welsh hogi (“to sharpen, hone”), Latin aciēs (“sharp”), acus (“needle”), Latvian ašs, ass (“sharp”), Ancient Greek ἀκίς (akís, “needle”), ἀκμή (akmḗ, “point”), and Persian آس (âs, “grinding stone”)).

(graph theory) A connected pair of vertices in a graph.

aresta

in graph theory: any of the pairs of vertices in a graph


rooted

en-adj

rooted (comparative more rooted, superlative most rooted)

more rooted (comparative)
most rooted (superlative)

(mathematics, graph theory, of a tree or graph) Having a root.


component

Borrowed from Latin compōnēns, compōnēntis, present participle of compōnō (“assemble, put together”).

bor+

(graph theory) A connected subgraph that is not part of any larger connected subgraph.


chromatic

en-adj

chromatic (not generally comparable, comparative more chromatic, superlative most chromatic)

more chromatic (comparative)
most chromatic (superlative)

Borrowed from French chromatique (“chromatic”) or directly from its etymon Latin chrōmaticus, from Ancient Greek χρωματικός (khrōmatikós, “relating to colour; one of the three types of tetrachord in Greek music”), from χρῶμα (khrôma, “colour; pigment; chromatic scale in music; music”) (ultimately from Proto-Indo-European *gʰer- (“to grind; to rub; to stroke; to remove”), perhaps in the sense of the grinding of pigments) + -τῐκός (-tĭkós, suffix forming adjectives); analysable as chroma + -tic.

der

LL-Q1860 (eng)-I learned some phrases-chromatic.wav

(not comparable, graph theory) Relating to colorings of graphs.

Uses relating to colour
Relating to colorings of graphs.


converse

From Latin conversus (“turned around”), past participle of converto (“turn about”).


cage

→ Zulu: ikheji

From Middle English cage, from Old French cage, from Latin cavea. Doublet of cadge and cavea and related to jail.

(graph theory) A regular graph that has as few vertices as possible for its girth.


pebble

en-verb

pebble (third-person singular simple present pebbles, present participle pebbling, simple past and past participle pebbled)

pebbles (present singular third-person)
pebbling (participle present)
pebbled (participle past)
pebbled (past)

From Middle English pibel (also in pibleston), from Old English papolstān (“pebble-stone”), from Old English *papol, *pyppel, *pæbbel of unknown origin + Old English stān. Compare Albanian popël.

unk

unknown

(transitive, graph theory) To place a pebble at (a vertex of a graph) according to certain rules, in a pebble game.


tour

From Old French tour, tourn, from the verb torner, tourner.

tor (pour–poor merger, horse–hoarse merger)

taw (pour–poor merger, horse–hoarse merger, non-rhotic)


girth

en-noun

girth (countable and uncountable, plural girths)

From Middle English girth, gerth, gyrth, from Old Norse gjǫrð, from Proto-Germanic *gerdō, from Proto-Indo-European *gʰerdʰ- (“to encircle, enclose; belt”). Cognate with Gothic 𐌲𐌰𐌹𐍂𐌳𐌰 (gairda), Icelandic gjörð. Also related to German Gurt, English gird, Albanian ngërthej (“to tie, bind, fasten”).

cog

(graph theory) The length of the shortest cycle in a graph.


circumference

From Latin circumferentia, from circum (“around”) + ferō (“I carry”). Displaced native Old English ymbgang.

(graph theory) The length of the longest cycle of a graph.


diameter

diameters (plural)
diametre (alternative)

From Old French diametre (French diamètre), from Latin diametrus, from Ancient Greek διάμετρος (diámetros) (γραμμή (grammḗ)) (diametros grammē, “line measuring across”), from διά (diá, “across”) + μέτρον (métron, “measure”). By surface analysis, dia- + -meter.

(graph theory) The maximum eccentricity over all vertices in a graph.


neighborhood

en-noun

neighborhood (countable and uncountable, plural neighborhoods)

neighborhoods (plural)
neighbourhood (alternative)

From an alteration of earlier neighborred (“neighborhood”), from Middle English neȝeburredde, neheborreden, equivalent to neighbor + -red; the term being interpreted as neighbor + -hood. For change in suffix (-red to -hood), compare brotherhood.
Cognates
Dutch nabijheid (common in modern language), Dutch naburigheid (uncommon in modern language).

veïnat

topology: set containing an open set which contains some specified point

vizinhança

topology: set containing an open ball which contains a specified point

(graph theory) The set of all the vertices adjacent to a given vertex.

In fact, it looks at the number of states and the neighborhood of the rule (determined by the filename), and decides whether to make it a lookup-table, or a "computed-function" rule.

1990 July 9, David Hiebeler, “Languages for programming cellular automata”, in comp.theory.cell-automata (Usenet):

Universal: Is able to simulate other CA, the neighborhood size may be limited but the number of cell value should be unlimited (big neighborhoods can be transformed into multivalued cells).

2005 September 7, IzI, “reversible universal 1D CA?”, in comp.theory.cell-automata (Usenet):

I've seen this space colloqually referred to as MAP (presumably since it maps a 3x3 neighborhood into a future cell state), or more precisely and if you want to be pedantic, since there are a lot of variants of cellular automata: 2D Range-1 Moore neighborhood 2-state (non-totalistic) cellular automata (regular euclidean grid implied, although some people explore toroidal configurations, nonstandard tilings, or arbitrary graphs).

2022 February 11, Mateon1, “Game of Life with real 8 neighbors”, in comp.theory.cell-automata (Usenet):

(cellular automata) The set of all cells near a given cell used to determine that cell's state in the next generation.


reverse

From Middle English revers, from Anglo-Norman revers, Middle French revers, and their source, Latin reversus, perfect passive participle of reversō, from re- + versō. Doublet of revers.


clique

Borrowed from French clique, ultimately of imitative origin. Influenced by "claque", though this may have happened in French rather than in English.

claque

another type of ingroup of people with biased interests

The problem of finding the largest clique in an arbitrary graph is NP-complete.

(graph theory) A subgraph isomorphic to a complete graph.


strength

strength (countable and uncountable, plural strengths)

[st̠͡ɹ̠ɛŋkθ]

[st̠͡ɹ̠ɛn̪θ]

[s̠t͡ʃɹ̥ɛn̪θ]

[st̠͡ɹ̠ɪŋkθ]

[st̠͡ɹ̠ɛɪŋkθ]

[st̠͡ɹ̠eɪŋkθ]

From Middle English strengthe, from Old English strengþu (“strength”), from Proto-West Germanic *strangiþu (“strongness; strength”), equivalent to strong + -th. Cognate with Dutch strengte (“strength”), German Low German Strengde, Strengte (“harshness; rigidity; strictness; severity”).

inh

(graph theory) The minimum ratio of the number of edges removed from a given graph to components created, over all possible removals.


condensation

en-noun

condensation (countable and uncountable, plural condensations)

From condense + -ation, borrowed from Latin condēnsātiō, condēnsātiōnem.

directed acyclic graph
directed acyclic graph

strongly connected component
strongly connected component

(graph theory, countable) For a given directed graph G, a directed acyclic graph with one vertex for each strongly connected component of G, and an edge connecting pairs of components that contain the two endpoints of at least one edge in G.


deck

From Middle English dekke, borrowed from Middle Dutch dec (“roof, covering”), from Middle Dutch decken, from Old Dutch thecken, from Proto-West Germanic *þakkjan, from Proto-Germanic *þakjaną. Formed the same: German Decke (“covering, blanket”). Doublet of thatch and thack.

rearrange the deck chairs on the Titanic

shuffle the chairs on the deck of the Titanic

Meronym: card

(graph theory) The multiset of graphs formed from a single graph by deleting a single vertex in all possible ways.


flap

From Middle English flap, flappe (“a slap; blow; buffet; fly-flap; something flexible or loose; flap”), related to Saterland Frisian Flappert (“wing, flipper”), Middle Dutch flabbe (“a blow; slap on the face; fly-flap; flap”) (modern Dutch flap (“flap”)), Middle Low German flabbe, vlabbe, flebbe, from the verb (see below). Related also to English flab and flabby.

cog

(graph theory) A connected component of the induced subgraph formed by deleting a set of vertices.


node

→ Irish: nód

From Middle English node, borrowed from Latin nōdus. Doublet of knot, knout, and nodus.

(graph theory) A vertex or a leaf in a graph of a network, or other element in a data structure.


sink

a bathroom sink sink (canonical)
sinks (plural)

From Middle English synken, from Old English sincan, from Proto-West Germanic *sinkwan, from Proto-Germanic *sinkwaną, from Proto-Indo-European *sengʷ- (“to fall, sink”).
Compare West Frisian sinke, Low German sinken, Dutch zinken, German sinken, Danish and Norwegian Bokmål synke, Swedish sjunka. In the causative sense, it replaced Old English senċan (“make sink”) from Proto-Germanic *sankwijaną.

der

transportation network
transportation network

(graph theory) A destination vertex in a transportation network.

(graph theory) A node in directed graph for which all of its edges go into it; one with no outgoing edges.


isthmus

Borrowing from Latin isthmus (“a strip of land between two seas”), from Ancient Greek ῐ̓σθμός (ĭsthmós, “neck, narrow passage”), possibly from εἶμῐ (eîmĭ, “to go”). Cognate to Old Norse eið (“isthmus”).

bor

(graph theory) An edge in a graph whose deletion increases the number of connected components of the graph.


coloring

en-noun

coloring (countable and uncountable, plural colorings)

colorings (plural)
colouring (alternative)

(graph theory) An assignment of a color to each vertex of a graph, usually such that no two vertices connected by an edge are given the same color.


transpose

en-verb

transpose (third-person singular simple present transposes, present participle transposing, simple past and past participle transposed)

transposes (present singular third-person)
transposing (participle present)
transposed (participle past)
transposed (past)

From Middle English transposen, from Old French transposer, from Latin trānspositus, perfect passive participle of trānspōnō (“to put across”), from trāns (“across”) + pōnō (“to put”).

(transitive, graph theory) To reverse the direction of every edge of (a graph).


transpose

(graph theory) Created by transposing a specified graph.


transpose

(graph theory) A graph whose every edge has had its direction reversed.


bandwidth

en-noun

bandwidth (countable and uncountable, plural bandwidths)

(graph theory) The minimum, over all orderings of vertices of a given graph, of the length of the longest edge.


dominate

en-verb

dominate (third-person singular simple present dominates, present participle dominating, simple past and past participle dominated)

dominates (present singular third-person)
dominating (participle present)
dominated (participle past)
dominated (past)

From Latin dominātus, perfect active participle of dominor (“rule, have dominion”), from dominus (“lord, master”); see dominus.

(computing, graph theory, linguistics) To precede another node of a directed graph in all paths from the start of the graph to the other node.


loop

From Middle English loupe (“noose, loop”), earlier lowp-knot (“loop-knot”), of North Germanic origin, from Old Norse hlaup (“a run”), used in the sense of a "running knot", from hlaupa (“to leap”), ultimately from Proto-Germanic *hlaupaną (“to leap, run”). Compare Swedish löp-knut (“loop-knot”), Danish løb-knude (“a running knot”), Danish løb (“a course”). More at leap. The verb is derived from the noun.

der

(graph theory) An edge that begins and ends on the same vertex.

silmukka

edge that begins and ends on the same vertex of a graph


claw

From Middle English clawe, from Old English clawu, from Proto-Germanic *klawō. Compare West Frisian klau, Dutch klauw, German Klaue, Danish klo, Norwegian klo, and Swedish klo.

(graph theory) A tree with one internal vertex and three leaves.


planar

en-adj

planar (comparative more planar, superlative most planar)

more planar (comparative)
most planar (superlative)

From Late Latin plānārius (“relating to a plane”), derived from Latin plānus (“flat”, “level”), equivalent to plane + -ar, ultimately from Proto-Indo-European *pleh₂- (“flat”).

bor

A complete graph with more than four nodes is never planar.

(graph theory, of a graph) Able to be embedded in the plane with no edges intersecting.


BST

en-noun

BST (countable and uncountable, plural BSTs)

(computing, graph theory) Initialism of binary search tree.


undirected graph

undirected graph (plural undirected graphs)

(graph theory) A graph in which the edges are not ordered, so the edge (a, b) is identical to the edge (b, a).


directed graph

Coordinate term: oriented graph

A directed graph (A, R) is a set of vertices A together with an incidence relation R: if aRb then there is an edge going from A to B.

(graph theory) A graph in which the edges are ordered pairs, so that, if the edge (a, b) is in the graph, the edge (b, a) need not be in the graph and is distinct from (a, b) if it is.


directed edge

(graph theory) An edge of a directed graph.


thickness

thickness (countable and uncountable, plural thicknesses)

mental acuity

antonym(s) of “property of being stupid”

From Middle English thikkenesse, thiknesse, from Old English þicnes (“thickness, viscosity, density, hardness; obscurity, cloud, darkness; thicket; depth, a thick body, anything thick or heavy”), from Proto-West Germanic *þikkwīnassī (“thickness”), equivalent to thick + -ness. Cognate with West Frisian tsjokkens (“thickness”), Old High German dickinessī, dikkinissi, diknissi (“thickness, density”). Eclipsed non-native Middle English crassitude (“thickness”) from Latin crassitūdō (“thickness”).

inh

(graph theory, countable) The minimum number of planar subgraphs which a given graph can decompose into.


bramble

From Middle English brembel, from Old English bræmbel, from earlier brǣmel, brēmel, from dialectal Proto-West Germanic *brāmil, diminutive of *brām (English broom).

(graph theory) A collection of mutually touching connected subgraphs, where two subgraphs touch if they share a vertex or each includes one endpoint of an edge.


bipartite

From Latin bipartītus (“bisected”), perfect passive participle of bipartiō (“I divide into two parts, bisect”).

(graph theory, of a graph) Having vertices that can be divided into two independent sets (see bigraph)


connected

en-adj

connected (comparative more connected, superlative most connected)

more connected (comparative)
most connected (superlative)

In a connected graph, there is no section (proper subset that includes all edges from each vertex in said subset) of the graph that is isolated from the rest.

(mathematics, graph theory, of a graph) Having a path, either directed or undirected, connecting every pair of vertices.

sammenhængende

graph theory: having a path connecting every pair of vertices


directed

directed (comparative more directed, superlative most directed)

more directed (comparative)
most directed (superlative)

(graph theory) Having the properties of a directed graph.


marking

en-noun

marking (countable and uncountable, plural markings)

From Middle English marking, merking, merkunge, from Old English mearcung, from Proto-West Germanic *markungu, equivalent to mark + -ing.

(graph theory) Any configuration of a Petri net with a number of marks or tokens distributed across it.


incidence matrix

incidence matrix (plural incidence matrices or incidence matrixes)

incidence matrices (plural)
incidence matrixes (plural)

(graph theory) A matrix showing the relationship between two classes of objects.


pseudograph

LL-Q1860 (eng)-Flame, not lame-pseudograph.wav

(graph theory) A graph that may contain loops as well as multiple edges between vertices


valency

valency (countable and uncountable, plural valencies)

From Late Latin valentia and Latin valentia (“bodily strength; health; vigour”) + English -y (suffix forming abstract nouns denoting a condition, quality, or state). Valentia is derived from valēns (“healthy, strong, vigorous”) + -ia (suffix forming feminine abstract nouns); while valēns is the present active participle of valeō (“to be healthy, sound, or well; to be strong; to have influence or power, etc.”), ultimately from Proto-Indo-European *h₂welh₁- (“to rule; powerful, strong”).
Sense 1 (“combining capacity of an atom”) and sense 3 (“number of arguments a verb can have”) are possibly from valence + -y.

der

(countable, graph theory) The number of edges connected to a vertex in a graph.


indegree

/ˈɪndəˌɡɹiː/

(graph theory) The number of edges directed into a vertex in a directed graph

入度

the number of edges directed into a vertex in a directed graph


outdegree

/ˈaʊtdəˌɡɹiː/

(graph theory) The number of edges directed out of a vertex in a directed graph.


chromatic number

en-noun

chromatic number (plural chromatic numbers)

The chromatic number of a complete graph K#95;n is n; the chromatic number of a bipartite graph K#95;#123;n,m#125; is 2.

The chromatic number of a graph G is the minimum value of k for which G is k-colourable, and is denoted by #92;chi(G).[…]A more essential use of the chromatic number was made by Gallai (1968a) and Roy (1967), who discovered a simple relationship between the chromatic number of a digraph and the length of a longest directed path in the digraph, where the chromatic number #92;chi(D) of a digraph D is defined to be the chromatic number of its underlying graph G(D).

1995, J. A. Bondy, “1: Basic Graph Theory: Paths and Circuits”, in Ronald L. Graham, Martin Grötschel, László Lovász, editors, Handbook of Combinatorics, Volume 1, Elsevier (North-Holland), page 48:

2004, Monia Discepoli, Ivan Gerace, Riccardo Mariani, Andrea Remigi, A Spectral Technique to Solve the Chromatic Number Problem in Circulant Graphs, Antonio Laganà, et al. (editors), Computational Science and Its Applications, ICCSA 2004: International Conference, Proceedings, Part 3, Springer, LNCS 3045, page 745,
The CHROMATIC NUMBER is the minimum number of colors by means of which it is possible to color a graph in such a way that each vertex has a different color with respect to the adjacent vertices. Such a problem is an NP-hard problem [14] and [it] is even hard to obtain a good approximation of the solution in a polynomial time [17]. Although in a lot of computational problems the cost decreases when these problems are restricted to circulant graphs [6, 9], the CHROMATIC NUMBER problem is NP-hard even restrecting to circulant graphs [9]. Moreover the problem of finding a good approximation of the CHROMATIC NUMBER problem on circulant graphs is also NP-hard.

2009, Gary Chartrand, Ping Zhang, Chromatic Graph Theory, Taylor & Francis Group (CRC Press / Chapman & Hall), page 149,
There is no general formula for the chromatic number of a graph. Consequently, we will often be concerned and must be content with (1) determining the chromatic number of some classes of interest and (2) determining upper and/or lower bounds for the chromatic number of a graph.

(graph theory) The smallest number of colours needed to colour a given graph (i.e., to assign a colour to each vertex such that no two vertices connected by an edge have the same colour).

kromatikus szám

smallest number of colours needed to colour a graph

vertex chromatic number

smallest number of colours needed to colour the vertices of a graph

used to differentiate from edge chromatic number


eccentricity

eccentricity (countable and uncountable, plural eccentricities)

excentricitat

a ratio between distances in a conic section

(graph theory) The farthest distance from a vertex to any other vertex.


weighted

en-adj

weighted (comparative more weighted, superlative most weighted)

more weighted (comparative)
most weighted (superlative)

(graph theory, of a graph) having values assigned to its edges


acyclic

acyclic (comparative more acyclic, superlative most acyclic)

more acyclic (comparative)
most acyclic (superlative)

(graph theory, of a graph) Containing no cycles.


MST

minimum spanning tree
w:minimum spanning tree

(graph theory) Initialism of minimum spanning tree.


dendrimer

(graph theory) A graph formed of branches from a central core.


subgraph

(graph theory) A graph or network that makes up part of a larger graph or network.


matching

(graph theory) A set of independent edges in a given graph, i.e. a set of edges which do not intersect, such that pairs of vertices are "matched" to each other one to one.


caterpillar tree

en-noun

caterpillar tree (plural caterpillar trees)

(graph theory) A tree consisting of only a path (the spine or stalk of the tree) and vertices directly connected to (i.e. one edge away from) that path; a tree whose vertices with a degree of at least 3 are all surrounded by at most two vertices of degree two or greater.


Tutte matrix

Tutte matrix (plural Tutte matrices or Tutte matrixes)

Tutte matrices (plural)
Tutte matrixes (plural)

From the name of W. T. Tutte (1917-2002), British/Canadian mathematician, and matrix.

(graph theory) A matrix used to determine whether all of the edges of a graph can be traversed without visiting a vertex more than once.


path length

(graph theory) The number of edges traversed in a given path in a graph.


incidence

incidence (countable and uncountable, plural incidences)

From Middle French incidence, from Medieval Latin incidentia (“a falling upon”), from Latin incidens, present participle of incidere (“to fall upon”), from in (“on”) + cadere (“to fall”).

der

(graph theory) The relation between an edge of a graph and one of the vertices it connects.


complete graph

(graph theory) A graph where every pair of vertices is connected by an edge.


graph theorist

(graph theory) A mathematician or computer scientist who specializes in graph theory


chordal

(graph theory) For a graph, in which all cycles of four or more vertices have a chord.


splicer

uniform spanning trees
uniform spanning tree

(graph theory) A union of uniform spanning trees.


centroid

LL-Q1860 (eng)-Flame, not lame-centroid.wav

From centre + -oid. From 1844, used as a replacement for the older terms "centre of gravity" and "centre of mass" in situations described in purely geometrical terms, and subsequently used for further generalisations.

形心

mean position of points in a geometrical figure — see also center of gravity, barycenter

barycentre

centre of gravity of a uniform, rigid object

1974 [Prentice-Hall], Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, 2017, Dover, page 248,
Just as in the case of centers of a tree (Section 3-4), it can be shown that every tree has either one centroid or two centroids. It can also be shown that if a tree has two centroids, the centroids are adjacent.

2009, Hao Yuan, Patrick Eugster, An Efficient Algorithm for Solving the Dyck-CFL Reachability Problem on Trees, Giuseppe Castagna (editor), Programming Languages and Systems: 18th European Symposium, Proceedings, Springer, LNCS 5502, page 186,
A node x in a tree T is called a centroid of T if the removal of x will make the size of each remaining connected component no greater than |T|/2. A tree may have at most two centroids, and if there are two then one must be a neighbor of the other [6, 5]. Throughout this paper, we specify the centroid to be the one whose numbering is lexicographically smaller (i.e, we number the nodes from 1 to n). There exists a linear time algorithm to compute the centroid of a tree due to the work of Goldman [21]. We use operatorname CT(T) to denote the centroid of T computed by the linear time algorithm.

(graph theory, of a tree) Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.


betweenness

en-noun

betweenness (countable and uncountable, plural betweennesses)

This is done by computing all the betweennesses of all edges and then looking for the ones with the highest values.

2010, David Easley, Networks, Crowds, and Markets: Reasoning About a Highly Connected World:

(graph theory, countable) A measure of the number of geodesic paths through a node or edge.


extractor

LL-Q1860 (eng)-Flame, not lame-extractor.wav

(graph theory) A particular kind of bipartite graph.


traceable

en-adj

traceable (comparative more traceable, superlative most traceable)

more traceable (comparative)
most traceable (superlative)

/ˈt͡ʃɹeɪsəbəl/

(graph theory, not comparable) Containing a Hamiltonian path.


choosability

(chiefly graph theory) The property of being choosable.


arborescence

(graph theory) A directed rooted tree in which all vertices can be reached from the root.


coclique

(graph theory) a subgraph whose complement is a clique, i.e. an independent set


independent set

en-noun

independent set (plural independent sets)

(graph theory) a set of vertices of a graph, such that no pair of them are adjacent to each other; in other words, a set of vertices which are all "independent" of each other


vertex cover

(graph theory) a set of vertices which touch all the edges of a graph


edge cover

(graph theory) A set of edges which touch all the vertices of a graph.


covering number

covering number (plural covering numbers)

(graph theory) The number of vertices in a minimum vertex cover of a graph, often denoted as τ=τ(G).


edge covering number

edge covering number (plural edge covering numbers)

(graph theory) The number of edges in a minimum edge cover of a graph, often denoted as ρ=ρ(G).


matching number

matching number (plural matching numbers)

(graph theory) the number of edges in a maximum matching, often denoted ν=ν(G)


independence number

independence number (plural independence numbers)

(graph theory) The number of vertices in a maximum independent set of a given graph, often denoted as α=α(G).


dominating set

(graph theory) A set of vertices of a graph, such that each vertex in that graph is either in that set or adjacent to a vertex in that set.


domination number

domination number (plural domination numbers)

(graph theory) the number of vertices in a minimum dominating set of a given graph, often denoted as γ=γ(G)


dominator

dominators (plural)
dominatour (alternative)

LL-Q1860 (eng)-Flame, not lame-dominator.wav

(graph theory) A node that dominates another.

One who, or that which, dominates.
A node that dominates another.


collider

LL-Q1860 (eng)-Flame, not lame-collider.wav

(graph theory) A node in a causal graph that has at least two incoming edges.


strongly connected component

strongly connected component (plural strongly connected components)

(graph theory) Given a directed graph, a maximal strongly connected subgraph.


strongly connected

(graph theory) Of a directed graph, such that for every pair of vertices u and v there is a path from u to v and a path from v to u.

(graph theory) Of a directed graph, such that for every pair of vertices u and v there is a directed path either from u to v or from v to u.


connected component

connected component (plural connected components)

(topology and graph theory) A connected subset that is, moreover, maximal with respect to being connected.


digon

From di- (prefix meaning ‘two’) + -gon (suffix forming the names of plane figures containing a given number of angles).

confix

monogon · digon · trigon · tetragon · pentagon · hexagon · heptagon · octagon · nonagon · decagon · undecagon · dodecagon · see also Category:English terms suffixed with -gon

A pair of parallel undirected edges in a multigraph.

A pair of antiparallel edges in a directed graph.


expander

(graph theory) A kind of sparse graph with strong connectivity properties.


tricomponent

(graph theory) A component having three nodes.


polytree

(graph theory) a graph with at most one undirected path between any two vertices. In other words, a directed acyclic graph (DAG) for which there are no undirected cycles either.


pseudoforest

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(graph theory) an undirected graph in which every connected component has at most one cycle


Hamiltonian

(mathematics, graph theory, of a cycle/path) That visits each vertex exactly once.

Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large.

2016, Jacky Cresson, Jordy Palafox, “Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat”, in arXiv:

(mathematics, graph theory, of a graph) Containing a Hamiltonian cycle.


connected graph

en-noun

connected graph (plural connected graphs)

(graph theory) A graph in which there is a route of edges and nodes connecting any two nodes.


cyclomatic

(graph theory) Used to describe the number of edges that must be removed from a graph to ensure that no graph cycle remains; equal to the number of edges, minus the number of nodes plus one.


multigraph

(graph theory) A set V (whose elements are called vertices or nodes), taken together with a multiset E, each of whose elements (called an edge or line) is a cardinality-two multisubset of V.

(graph theory, less commonly) A set V (as before), taken together with a multiset E, each of whose elements is a cardinality-two subset of V.


subtree

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(mathematics, computer science, graph theory) A tree wholly contained in another.

podstrom

mathematics, computer science: a tree wholly contained in another


antichain

First of all, Zorn's Lemma implies that every uncountable antichain in T is contained in a maximal uncountable antichain. So it suffices to make sure that T has no maximal uncountable antichains.

1997, Winfried Just, Martin Weese, Discovering Modern Set Theory II: Set-Theoretic Tools for Every Mathematician, American Mathematical Society, page 140:

2013, Vijay K. Garg, Maximal Antichain Lattice Algorithms for Distributed Computations, Proceedings, Davide Frey, Michel Raynal, Saswati Sarkar, Rudrapatna K. Shyamasundar, Prasun Sinha (editors), Distributed Computing and Networking: 14th International Conference, ICDCN, Springer, LNCS 7730, page 245,
We first define three different but isomorphic lattices: the lattice of maximal antichain ideals, the lattice of maximal antichains and the lattice of strict ideals.

2014, Martin Aigner, Günter M. Ziegler, Proofs from THE BOOK, Springer, 5th Edition, page 199,
In 1928 Emanuel Sperner asked and answered the following question: Suppose we are given the set N=1,2,3,…,n. Call a family ℱ of subsets of N, which has partial order ⊆]) an antichain if no set of ℱ contains another set of the family ℱ. What is the size of a largest antichain? Clearly, the family ℱₖ of all k-sets satisfies the antichain property with |ℱₖ|=\binomnk. Looking at the maximum of the binomial coefficients (see page 14) we conclude that there is an antichain of size \binomn[n/2]= max ₖ\binomnk. Sperner's theorem now asserts that there are no larger ones.

partially ordered set
partially ordered set

(set theory, order theory, graph theory) A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.


hypohamiltonian

(graph theory) Of a graph, not containing a Hamiltonian cycle but such that the removal of any single vertex produces a Hamiltonian graph.


Hamiltonian path

Hamiltonian path (plural Hamiltonian paths)

Named after William Rowan Hamilton (1805-1865), Irish mathematician.

(graph theory) A path through a graph which visits each vertex exactly once.

Hamiltonpad

path which visits each vertex exactly once


Hamiltonian cycle

Hamiltonian cycle (plural Hamiltonian cycles)

(graph theory) A Hamiltonian path with an additional connection between the first and last vertices visited, forming a cycle.

hamiltonkreds

graph theory: a cycle visiting all vertices once


Hamiltonian graph

Hamiltonian graph (plural Hamiltonian graphs)

(graph theory) A graph for which there is a Hamiltonian cycle.


chorded

a chorded cycle


quadrivalent

In graph theory terms, a regular projection of a knot, or knot diagram is thus a quadrivalent planar graph with over/under-decorated vertices.

2020 January 3, Wikipedia contributors, “Knot (mathematics)”, in English Wikipedia, Wikimedia Foundation:

(graph theory) Said of a graph: that all of its vertices have degree four.


hypergraph

(graph theory) A generalization of a graph, in which edges can connect any number of vertices.


empty graph

The empty graph with n vertices is denoted as Eₙ.

(graph theory) A graph with vertices but no edges.


undirected path

undirected path (plural undirected paths)

A path x→y←z is an undirected path.

(graph theory) In a directed graph, a path in which the edges are not all oriented in the same direction.


directed path

A path x→y→z is a directed path.

(graph theory) In a directed graph, a path in which the edges are all oriented in the same direction.


superconnected

en-adj

superconnected (comparative more superconnected, superlative most superconnected)

more superconnected (comparative)
most superconnected (superlative)

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For a superconnected probe interval graph G, a tree 4-spanner can be constructed easily.

2003, H. L. Bodlaender, Graph-theoretic concepts in computer science: 29th International Workshop:

(graph theory, of a graph) Whose every minimum vertex cut leads to isolated vertices.


hyperedge

(graph theory) The equivalent of a graph's edge in a hypergraph.


hypervertex

(graph theory) The equivalent of a graph's vertex in a hypergraph.


noneven

(graph theory) Of a digraph, having no cycles of even weight


arboricity

en-noun

arboricity (countable and uncountable, plural arboricities)

(graph theory) The minimum number of forests into which the edges of an undirected graph may be partitioned.


antihole

(graph theory) Clipping of graph antihole.


biconnected

(graph theory) Describing a connected graph from which two vertices must be removed for it to become disconnected.


outerplanar

(graph theory) Having a planar embedding such that the vertices lie on a circle and the edges lie inside that circle.


bicomponent

(graph theory) A component having two nodes.


sparsifier

(graph theory) A graph that is a sparse version of another.


Eulerian

(graph theory) Having an Eulerian circuit.


subpath

(graph theory) A path making up part of a larger path (the superpath).


superpath

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(graph theory) The path that contains a particular subpath.


multidigraph

(graph theory) A directed graph that is permitted to have multiple arcs connecting the same source and target nodes.


antiregular

(graph theory) Of a graph: having either zero or two vertices of the same degree.


pathwidth

(graph theory) A measure of a path decomposition of a graph.


centroidal

(graph theory, of a tree) Having a single centroid.


unicyclic

(graph theory, of a graph) Having a single cycle.


depth-first search

depth-first search (countable and uncountable, plural depth-first searches)

Coordinate term: breadth-first search

(graph theory) An algorithm for traversing a tree or graph where one starts at the root and explores as far as possible along each branch before backtracking.

syvyyshaku

algorithm where one starts at the root and explores as far as possible down before going up


weighted graph

(graph theory) A graph that associates a weight (usually a real number) with every edge in the graph.


clique number

(graph theory) The number of vertices in a maximum clique of a given graph.

Clique (graph theory)
Glossary of graph theory


Bellman-Ford algorithm

Bellman-Ford algorithm (plural Bellman-Ford algorithms)

Named after its developers, Richard Bellman and L. R. Ford, Jr.

Dijkstra's algorithm
Dijkstra's algorithm

(graph theory, computing) An algorithm that computes single-source shortest paths in a weighted digraph, capable (unlike the faster Dijkstra's algorithm) of handling graphs with negative edge weights.

Bellman-Ford algorithm
L. R. Ford, Jr.
Richard Bellman


Dijkstra's algorithm

/ˈdaɪkstɹəz ˈælɡəɹɪðəm/

(graph theory) An algorithm that computes single-source shortest paths in a weighted digraph.


hyperarc

(graph theory) A directed edge in a hypergraph.


biclique

(graph theory) A special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set.


breadth-first search

breadth-first search (countable and uncountable, plural breadth-first searches)

Coordinate term: depth-first search

(graph theory) A search algorithm that begins at the root node and explores all the neighboring nodes.


pseudodigraph

(graph theory) A graph that resembles a directed graph but violates one of the normal rules, as for example by including a directed loop.


Steiner point

(graph theory) An extra vertex that is not a member of the input.


dedecoration

Dedecoration did not produce any advantages in observing the size of the displacement of dislocations.

Applying the star-triangle and dedecoration transformations[…]

(graph theory) Decimation (the elimination of points from a lattice); the inverse of decoration.


line graph

(graph theory) A graph L(G) which is derived from a given non-oriented graph G such that the vertices of L(G) represent edges of G and so that a clique in L(G) represents a common end-vertex shared by a set of represented edges. (A star subgraph in G transforms into a clique in L(G).)

Suppose that a graph G has vertices A, B, C, and D such that A is adjacent to each of B, C, and D, but {B, C, D} is an independent set. Then G cannot be a line graph.

A graph which is the line graph (in the above sense) of some other graph.


treeness

…such a tree can be built up incrementally by adding the shortest edge not yet explored, which also maintains treeness (acyclicity).

1998, Joseph O'Rourke, Computational Geometry in C, 2nd edition, Cambridge University Press, →ISBN, page 174:

…every link that gives rise to a cycle into the graph (viz., that destroys the graph’s “treeness”) is eliminated….

2010, Massimo Buscema, Pier L. Sacco, “Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG)”, in Vittorio Capecchi et al., editors, Applications of Mathematics in Models, Artificial Neural Networks and Arts, Springer, →ISBN, page 265:

To save the treeness of discourse structure – and with that the supplied computational advantages – Egg and Redeker (2008) argue that many apparent crossed dependencies reflect anaphoric relations on the level of discourse cohesion…. They opt for a pure tree structure for discourse relations, keeping anaphoric relations apart.

2011, Matthias Irmer, Bridging Inferences, De Gruyter,, →ISBN, page 139:

(graph theory) The condition of being a tree; acyclicity and connectedness.


spanning tree

(graph theory) A tree structure which includes all vertices of a graph.

virityspuu

tree which includes all vertices of a graph


hypertree

(graph theory) A form of hypergraph based on trees.


Bethe lattice

(graph theory) A kind of connected cycle-free graph.


hypernode

(graph theory) A kind of graph whose node set can contain other graphs as well as basic nodes.


bouquet of circles

bouquet of circles (plural bouquets of circles)

(mathematics, graph theory) A graph with only one vertex.


wedge of circles

wedge of circles (plural wedges of circles)

(graph theory) A graph with only one vertex.


idom

(graph theory) Abbreviation of immediate dominator.


Desargues graph

Desargues graph (plural Desargues graphs)

(graph theory) A distance-transitive cubic graph with 20 vertices and 30 edges.


Petersen's theorem

(graph theory) The theorem stating that every cubic bridgeless graph contains a perfect matching.


semi-complete

(mathematics, graph theory) of or pertaining to a graph in which, for any two verticies u, v in the graph, there is another vertex w which is adjacent to both u and v (i.e. u,w,v is a path in that graph).


Ore's theorem

Proved in 1960 by Norwegian mathematician Øystein Ore.

(graph theory) A theorem that considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.


Veblen's theorem

(graph theory) A theorem stating that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree.


adjacency matrix

adjacency matrix (plural adjacency matrices or adjacency matrixes)

adjacency matrices (plural)
adjacency matrixes (plural)

(graph theory) A matrix showing which vertices of a graph are adjacent to which other vertices.


graphon

This bound almost matches the known upper bound for graphs and, in a certain sense, is the best possible for graphons.

2015, Jacob W. Cooper, Tomáš Kaiser, Daniel Kráľ, Jonathan A. Noel, “Weak regularity and finitely forcible graph limits”, in (Please provide the book title or journal name):

(mathematics, graph theory) The completion of the metric space of the set of finite graphs endowed with the cut metric.


ultrasparsifier

(graph theory) A form of sparsifier that makes a graph particularly sparse.


rectagraph

Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every 2-path lies in a unique quadrangle.

2015, Joanna B. Fawcett, “Locally triangular graphs and normal quotients of the n-cube”, in arXiv:

(graph theory) A triangle-free connected graph where any two vertices have 0 or 2 common neighbors.


triangle-free

undirected graph
undirected graph#English

(graph theory) Of an undirected graph in which no three vertices form a triangle of edges.


isoradial

The critical surface for random-cluster model with cluster-weight q#92;ge 4 on isoradial graphs is identified using parafermionic observables.

2015, Vincent Beffara, Hugo Duminil-Copin, Stanislav Smirnov, “On the critical parameters of the q>4 random-cluster model on isoradial graphs”, in arXiv:

(graph theory) Of a planar graph: where each face is inscribable in a circle of common radius.


pancyclic

(graph theory, of a graph) Containing cycless of every possible length (from 3 to the order of the graph).


dismantlability

(chiefly graph theory) The quality of being dismantlable.


dismantlable

We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere.

2015, Michal Adamaszek, “A note on independence complexes of chordal graphs and dismantling”, in arXiv:

(graph theory) The property of a graph such that its vertices can be listed in an order such that, for every vertex, the vertex is a subdominant vertex (has an adjacent vertex that is adjacent to every other vertex that it is adjacent to) in the induced subgraph generated by that vertex and all subsequent vertices.


subtournament

(graph theory) A tournament that forms part of another tournament.


Steiner tree

(graph theory) The minimum-weight connected subgraph of a graph that includes all the vertices of that graph.


isthmoid

(graph theory) A set of vertices of a graph after whose deletion the graph is no longer connected.


subtour

The resulting problem is solved to integer optimality, violated constraints (which are trivial to find) are added and the process is repeated until a feasible solution is found. In order to speed up the algorithm we pursue several attempts to find as many relevant subtours as possible.

2015, Ulrich Pferschy, Rostislav Stanek, “Generating subtour elimination constraints for the TSP from pure integer solutions”, in arXiv:

(graph theory) A tour that makes up part of a larger tour.


triconnected

(graph theory) Of a connected graph: needing three vertices removed for it to become disconnected.


thrackle

Scots term for a fouled fishing line, which Conway heard when visiting Scotland.

We prove that a thrackle drawing containing a standard musquash (standard n-gonal thrackle) cannot contain any other cycle of length three or five.

2016, Grace Misereh, Yuri Nikolayevsky, “Thrackles containing a standard musquash”, in arXiv:

(graph theory) An embedding of a graph in the plane, such that each edge is a Jordan arc and every pair of edges meet once.


plabic

Of course, as illustrated in the example above, merely reordering the face variables of a fixed plabic graph by an odd permutation will change the orientation of the resulting volume-form.

2016, Nima Arkani-Hamed, Grassmannian Geometry of Scattering Amplitudes, page 116:


laceable

(graph theory) Of a bipartite graph: having a possible Hamiltonian path between any two vertices from different partite sets.


laceability

(graph theory) The property of being laceable.


walktrap

We show that fastgreedy and walktrap community detection methods on weighted label co-occurence^([sic]) graphs are 85-92% more likely to yield better F1 scores than random partitioning.

2016, Piotr Szymański, Tomasz Kajdanowicz, Kristian Kersting, “How is a data-driven approach better than random choice in label space division for multi-label classification?”, in arXiv:

(graph theory) An algorithm for identifying communities in large networks using random walks.


cutwidth

(graph theory) The minimum number of edges that cross any cut between lower-numbered and higher-numbered vertices in an optimal linear arrangement of the vertices of a graph.


biconnectivity

(graph theory) The property of being biconnected.


Euler line

Euler lines (plural)
Euler's line (alternative)

Named for Swiss mathematician Leonhard Euler.

Theorem 2.1 A connected graph with even local degrees has an Euler line.

1961, Yale University, Graphs and Their Uses, page 25:

In defining an Euler graph, some authors drop the requirement that the Euler line be closed.

2009, J. P. Chauhan, Krishna's Applied Discrete Mathematics, page 279:

Euler lines mainly deal with the nature of connectivity in graphs. The concept of an Euler line is used to solve several puzzles and games.[…]A closed walk running through every edge of the graph G exactly once is called an Euler line.

2013, Bhavanari Satyanarayana, Kuncham Syam Prasad, Near Rings, Fuzzy Ideals, and Graph Theory, page 372:

(graph theory) An Eulerian path, a looped path through a graph that passes along every edge exactly once.


Hamiltonicity

(graph theory) The property of being Hamiltonian.


decycle

en-verb

decycle (third-person singular simple present decycles, present participle decycling, simple past and past participle decycled)

decycles (present singular third-person)
decycling (participle present)
decycled (participle past)
decycled (past)

In the decycling phase it removes or redirects some edges until the resulting graph is acyclic.

2009, Ioannis G. Tollis, Maurizio Patrignani, Graph Drawing: 16th International Symposium:

(graph theory, transitive) To remove the cycles from.


Herschel graph

From Herschel (“a surname”) + graph, after British astronomer Alexander Stewart Herschel (1836—1907), who identified the associated polyhedron (an enneahedron) as one for which there is no solution to the icosian game.

Select a suitable independent set / and use part (b) to show that the graph in Fig. 11.81 (known as the Herschel graph) has no Hamilton cycle.

1994, Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, page 587:

A bipartite graph like the Herschel graph of Figure 9.2 is also non-hamiltonian, but the algorithm is not likely to delete enough vertices to notice that it has a large separating set.

2004, William Kocay, Donald L. Kreher, Graphs, Algorithms, and Optimization, page 202:

2006, Michael S. Keane, Dee Denteneer, Frank Hollander, Evgeny Verbitskiy, Dynamics and Stochastics, Institute of Mathematical Statistics, Lecture Notes—Monograph Series, Volume 48, page 174,
It is difficult to control what loops may arise: for example the Herschel graph [3] shows that a convex polyhedron need not be Hamiltonian as a graph.

(mathematics, graph theory) A bipartite undirected graph with 11 vertices and 18 edges that is the smallest non-Hamiltonian polyhedral graph.


four color theorem

(graph theory) A theorem stating that given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions so that no two adjacent regions have the same color (adjacent being defined as two regions sharing a boundary, not counting corners, in which three or more regions share a boundary).


outedge

(graph theory) An outgoing edge in a digraph, i.e. one that leaves a particular node.


inedge

(graph theory) An incoming edge in a digraph, i.e. one that enters a particular node.


half-edge

(graph theory) An edge that is attached to only one node, rather than connecting two of them, or is connected in only one direction


Eppstein's algorithm

After US mathematician David Eppstein (born 1963).

(graph theory) An algorithm that finds a number of shortest paths (allowing cycles) connecting a given pair of vertices in a digraph.


antidirected

A digraph D is antistrong if it contains an antidirected (x,y)-trail starting and ending with a forward arc for every choice of x,y#92;inV(D).

2016, Jorgen Bang-Jensen, Stephane Bessy, Bill Jackson, Matthias Kriesell, “Antistrong digraphs”, in arXiv:

(graph theory) Having arcs that alternate between forward and backward arcs.


coflow

Furthermore, we give an O(#92;logn#47;#92;log#92;logn)-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here n is the number of network edges). We note that our task-based coflow scheduling problem is equivalent to the fully-flexible order scheduling problem on unrelated parallel machines for which no O(1)-factor approximation algorithm was known prior to this work. We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios..

2016, Hamidreza Jahanjou, Erez Kantor, Rajmohan Rajaraman, “Asymptotically Optimal Approximation Algorithms for Coflow Scheduling”, in arXiv:

(graph theory) Any of a series of flows that have a common source and destination


quasi-transitive

(graph theory, of a graph) Such that its vertex set can be partitioned into finitely many sets, so that there exists an automorphism mapping a vertex to another vertex if and only if the two vertices belong to the same set in that partition.


semi-transitive

(graph theory, of a graph) Such that there exists a finite vertex set so that for any vertex there exists another vertex in that finite set and an injective homomorphism of the graph that maps the second vertex to the first vertex.


nodeset

(computing, graph theory) A set of nodes.


Eulerian trail

(graph theory) a trail that contains each edge exactly once.


Eulerian circuit

en-noun

Eulerian circuit (plural Eulerian circuits)

(graph theory) A Eulerian trail that begins and ends at the same node.


comdag

Blend of combined + DAG (“directed acyclic graph”).

blend

(graph theory) A directed acyclic combined graph.


Turán's theorem

Named after the Hungarian mathematician Pál Turán.

(graph theory) A theorem stating that, among the n-vertex simple graphs with no (r + 1)-cliques, T(n, r) has the maximum number of edges.


block graph

(graph theory) A type of undirected graph in which every biconnected component (block) is a clique.


Floyd-Warshall algorithm

the Floyd-Warshall algorithm (canonical)

Named after Robert W. Floyd and Stephen Warshall.

(computer science, graph theory) An algorithm for finding shortest paths in a weighted graph with positive or negative edge weights (but with no negative cycles).


Menger's theorem

It was proved for edge-connectivity and vertex-connectivity by Karl Menger in 1927.

(graph theory) A characterization of the connectivity in finite undirected graphs in terms of the minimum number of disjoint paths that can be found between any pair of vertices.


Laplacian matrix

en-noun

Laplacian matrix (plural Laplacian matrices)

Named after Pierre-Simon, marquis de Laplace (1749 – 1827), a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

(graph theory) A square n×n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.


Cayley's formula

(graph theory) A formula for the number of spanning trees of a complete graph of n vertices: nⁿ⁻².


Moore graph

Named in 1960 by Hoffman and Singleton, after Edward F. Moore, who posed the question of describing and classifying these graphs.

(graph theory) A regular graph of degree d and diameter k whose number of vertices equals the upper bound 1+d∑ᵢ₌₀ᵏ⁻¹(d-1)ⁱ.


regular map

Morphism of algebraic varieties
Regular map (graph theory)

1990 [McGraw-Hill], Jay Kappraff, Connections: The Geometric Bridge Between Art and Science, 2001, World Scientific, page 141,
Just as there are only five regular maps on the sphere (or plane), there are only three classes of regular maps that can be created on a torus.

If n is finite, the regular map is a tessellation of the plane by congruent n-sided polygons, m of which meet at each vertex.

2010, Jozef Širáñ, Yan Wang, “Maps with highest level of symmetry that are even more symmetric than other such maps: Regular maps with largest exponent groups”, in Richard A. Brualdi, Samat Hedayat, Hadi Kharaghani, Gholamreza B. Khosrovshahi, Shahriar Shahriari, editors, Combinatorics and Graphs: The Twentieth Anniversary Conference of IPM Combinatorics, American Mathematical Society, page 98:

2013, Roman Nedela, Martin Škoviera, 7.6: Maps, Jonathan L. Gross, Jay Yellen, Ping Zhang (editors), Handbook of Graph Theory, 2nd Edition, CRC Press, page 845,
If M is a regular map of type p,q, then mathit Aut(M)≈Δ(p,q,2)/N for some normal subgroup N⊴Δ(p,q,2). Similar statements hold for the class of orientably regular maps and subgroups of Δ⁺ and Δ⁺(p,q,2).

(graph theory) A symmetric tessellation of a closed surface; a decomposition of a two-dimensional manifold into topological disks such that every flag (incident vertex-edge-face triple) can be transformed into any other flag by a symmetry (i.e., an automorphism) of the decomposition.


BFS

Coordinate term: DFS

breadth-first search
breadth-first search#English

(graph theory) Initialism of breadth-first search.


DFS

Coordinate term: BFS

depth-first search
depth-first search#English

(graph theory) Initialism of depth-first search.


iterative deepening search

iterative deepening search (countable and uncountable, plural iterative deepening searches)

breadth-first search
breadth-first search

(computer science, graph theory) A type of depth-first search in which each row of the tree is searched incrementally, simulating a breadth-first search with less memory usage.


anticycle

(graph theory) A cycle in the complement of a given graph.


directed acyclic graph

directed acyclic graph (plural directed acyclic graphs)

1995, Volker Turan, Weimin Chen, GLB-closures in Directed Acyclic Graphs and Their Applications, Ernst W. Mayr, Gunther Schmidt, Gottfried Tinhofer (editors), Graph-Theoretic Concepts in Computer Science: 20th International Workshop, Proceedings, Springer, LNCS 903, page 121,
A subset S of the vertices of a directed acyclic graph is called glb-closed, if it contains the greatest lower bounds of all pairs of vertices of S. […] Directed acyclic graphs are widely used in different areas of computer science.

In studying these properties, a distinction is made between directed acyclic graphs with directed edges and simple acyclic graphs with undirected edges.[…]A directed acyclic graph G#61;(V#59;R) is asymmetric and does not contain cycles.

2001, Peter J. Pahl, Rudolf Damrath, Mathematical Foundations of Computational Engineering: A Handbook, Springer, page 574:

2011, Michael Donders, Sara Miner More, Pavel Naumov, Information Flow on Directed Acyclic Graphs, Lev D. Beklemishev, Ruy de Queiroz (editors), Logic, Language, Information, and Computation: 18th International Workshop, Proceedings, Springer, LNAI 6642, page 95,
A logical system that describes the properties of this relation for an arbitrary fixed directed acyclic graph is introduced and proven to be complete and decidable.

(graph theory, computer science) A finite directed graph that contains no directed cycles.


acyclic digraph

acyclic digraph (plural acyclic digraphs)

1993, Suh-Ryung-Kim, The Competition Number and Its Variants, J. Gimbel, J.W. Kennedy, L.V. Quintas (editors), Quo Vadis, Graph Theory?: A Source Book for Challenges and Directions, Elsevier (North-Holland), page 313,
In the study of the competition graph of an acyclic digraph, there are two fundamental questions which were proposed by Roberts in 1978: One is to characterize the acyclic digraphs that have interval competition graphs and the other is to characterize the graphs which are competition graphs of acyclic digraphs.

2009, Tamara Mchedlidze, Antonios Symvonis, Crossing-Optimal Acyclic HP-Completion for Outerplanar st-Digraphs, Hung Q. Ngo (editor), Computing and Combinatorics: 15th Annual International Conference, Proceedings, Springer, LNCS 5609, page 76,
Determining whether a graph has a hamiltonian path or circuit is NP-complete [3]. The problem remains NP-complete for cubic planar graphs [3], for maximal planar graphs [9], and for planar digraphs [3]. It can be trivially solved in polynomial time for planar acyclic digraphs.

2018, Gregory Gutin, 3. Acyclic Digraphs, Jørgen Bang-Jensen, Gregory Gutin, Classes of Directed Graphs, Springer, page 125,
Acyclic digraphs form a well-studied family of digraphs of great interest in graph theory, algorithms and applications.

(graph theory, computer science) A directed acyclic graph, a finite directed graph that contains no directed cycles.


Robertson-Seymour theorem

the Robertson-Seymour theorem (canonical)

Named after mathematicians Neil Robertson and Paul D. Seymour, who proved it in a series of papers from 1983 to 2004.

(graph theory) A theorem stating that the undirected graphs, partially ordered by the graph-minor relationship, form a well-quasi-ordering.


Chinese postman problem

Chinese postman problem (plural Chinese postman problems)

Originally studied by the Chinese mathematician Kwan Mei-Ko in 1960, whose Chinese paper was translated into English in 1962. The name "Chinese postman problem" was coined in his honour, and is varyingly ascribed to Alan J. Goldman or Jack Edmonds, both of the US National Bureau of Standards.

(graph theory) The problem of finding the shortest closed path or circuit that visits every edge of a (connected) undirected graph.


regular graph

(graph theory) A graph whose vertices all have the same degree.


plane graph

(graph theory) An embedding of a planar graph in a plane.


cubic graph

(graph theory) A 3-regular graph; i.e., a graph whose every vertex has degree three.


dual graph

The edges of a dual graph are perpendicular, in some sense, to the edges of its original graph. The dual graph also has as many vertices and faces as its original graph has faces and vertices, respectively. Therefore the dual graph has the same Euler characteristic as its original graph.

(graph theory) A graph derived from some plane graph in such a way that the derived graph has a vertex corresponding to each face of the given graph, an edge corresponding to each edge of the given graph that is shared by a pair of distinct faces, and a self-loop for each edge of the given graph that is a border of the same face on both of its sides.


planar graph

(graph theory) A graph which can be embedded in a plane in such a way that its edges only intersect at vertices, i.e., they do not cross each other.


medial graph

The number of vertices of a medial graph is equal to the number of edges of its original graph, and the number of edges of a medial graph is equal to the sum of the degrees of the vertices of the original graph.

(graph theory) A graph derived from a given plane graph such that this derived graph has a vertex corresponding to each edge of the given graph, and such that for every “angle” (consecutive trio of edge, vertex, edge) along the border of a face of the given graph there is a corresponding edge which connects the vertices corresponding to the two edges that are part of that “angle”.


submarking

(graph theory) A subset of a marking of a Petri net.


topological sort

topological sort (plural topological sorts)

(graph theory, computer science) An ordering of the vertices of a directed graph such that if an edge goes from vertex u to vertex v then u precedes v in the ordering.


crown graph

(graph theory) An undirected graph with 2n vertices in the two sets { u₁, u₂, ..., uₙ } and { v₁, v₂, ..., vₙ } and with an edge from uᵢ to vⱼ whenever i ≠ j.


Hedetniemi's conjecture

Formulated by Stephen T. Hedetniemi in 1966.

(graph theory) A conjecture concerning the connection between graph coloring and the tensor product of graphs. A counterexample was found in 2019.


de Bruijn graph

de Bruijn graph (plural de Bruijn graphs)

Named after the Dutch mathematician Nicolaas Govert de Bruijn.

(graph theory) A kind of directed graph representing overlaps between sequences of symbols.


de Bruijn-Erdős theorem

Named after the mathematicians Nicolaas Govert de Bruijn and Paul Erdős.

(graph theory) A theorem stating that, when all finite subgraphs of an infinite graph can be colored using c colors, the same is true for the parent graph.


algebraic graph theory

algebraic graph theory (countable and uncountable, plural algebraic graph theories)

The three main branches of algebraic graph theory involve the use of linear algebra, the use of group theory and the study of graph invariants.

The last section introduces elementary algebraic graph theory which is then applied to electrical networks.

1979, Béla Bollobás, Graph Theory: An Introductory Course, Springer, page 26:

Several famous results in algebraic graph theory, including one of the oldest, are formulae for the numbers of spanning trees of certain graphs.

1993, Norman Biggs, Algebraic Graph Theory, 2nd edition, Cambridge University Press, page 38:

Graphs with diameter d and girth 2d#43;1 are known as Moore graphs. They were introduced by Hoffman and Singleton in a paper that can be viewed as one of the prime sources of algebraic graph theory.

2013, Chris Godsil, Gordon F. Royle, Algebraic Graph Theory, Springer, page 77:

(uncountable, mathematics, graph theory) The subbranch of graph theory in which algebraic methods are applied to problems about graphs.


snake-in-the-box problem

the snake-in-the-box problem (canonical)

(graph theory) The problem of finding the longest possible induced path in a hypercube.


cocoloring

cocolorings (plural)
cocolouring (alternative)

(graph theory) The assignment of a color to each vertex of a graph such that each color class forms an independent set in the graph or its complement.


Turán graph

(graph theory) A complete multipartite graph T(n,r) formed by partitioning a set of n vertices into r subsets, with sizes as equal as possible, and connecting two vertices by an edge if and only if they belong to different subsets.


anarboricity

From an- + arboricity. Coined by Ronald C. Read; the etymologically inaccurate Greek prefix an- was chosen to achieve a pun on the name of Ann Arbor, where the University of Michigan is based.

(graph theory) The maximum number of edge-disjoint cyclic subgraphs of a graph G whose union is G.


postdominator

(graph theory) A node that postdominates another.


postdominance

(graph theory) The property of a node that postdominates another.


postdominate

en-verb

postdominate (third-person singular simple present postdominates, present participle postdominating, simple past and past participle postdominated)

postdominates (present singular third-person)
postdominating (participle present)
postdominated (participle past)
postdominated (past)

(graph theory) A node z postdominates a node n if all paths to the exit node of the graph starting at n must go through z


Johnson's algorithm

(graph theory) An algorithm for finding the shortest paths between all pairs of vertices in an edge-weighted directed graph.


Zarankiewicz problem

Named after the Polish mathematician Kazimierz Zarankiewicz, who proposed several special cases of the problem in 1951.

(graph theory) An unsolved problem in mathematics, asking for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs of a given size.


Zarankiewicz function

Zarankiewicz problem
Zarankiewicz problem

(graph theory) The function for which the Zarankiewicz problem seeks a formula: z(m, n; s, t), denoting the largest possible number of edges in a bipartite graph G = (U, V, E) for which |U| = m and |V| = n, but which does not contain a subgraph of the form K_(s,t).


preferential attachment

en-noun

preferential attachment (plural preferential attachments)

Coined by Albert-László Barabási and Réka Albert.

Aided by preferential attachment and network effects (the phenomenon of a good or service becoming more valuable the more people who use it), a handful of winners emerge, overshadowing other available options.

2014, Astra Taylor, chapter 4, in The People's Platform: Taking Back Power and Culture in the Digital Age, Henry Holt and Company, →ISBN:

(graph theory) A positive feedback cycle where the more connected nodes in a graph are more likely to receive new links.


utility graph

In reference to the three utilities problem, which asks to draw the utility graph in the plane.

(graph theory) The graph K_(3,3), which has six vertices in two sets of three and nine edges such that every vertex in one set is connected to each vertex in the other.


complete bipartite graph

complete bipartite graph (plural complete bipartite graphs)

(graph theory) A biclique, a bipartite graph such that every vertex of one set is connected to every vertex of the other.


GCA

greatest common ancestor
greatest common ancestor#English

(graph theory) Initialism of greatest common ancestor.


coreachable

Further, non coreachable nodes are qualified as forbidden. The loop terminates when all forbidden markings (those initially declared and those newly identified) are processed.

2013, Marcello La Rosa, Pnina Soffer, Business Process Management Workshops: BPM 2012 International Workshops, Tallinn, Estonia, September 3, 2012, Revised Papers, page 118:

Two cycles are coreachable if there exists a path from any of them to the other one.

2018, Cezar Câmpeanu, Implementation and Application of Automata: 23rd International Conference, CIAA 2018, Charlottetown, PE, Canada, July 30 – August 2, 2018, Proceedings, page 77:

(graph theory) Mutually reachable, that is, for any two nodes n1 and n2, they are coreachable iff n1 is reachable from n2 and n2 is reachable from n1.


Coxeter graph

Named after Harold Scott MacDonald Coxeter.

(graph theory) A 3-regular graph with 28 vertices and 42 edges, one of the 13 known cubic distance-regular graphs.


s-t cut

(graph theory) A cut that requires the source and the sink to be in different subsets, and its cut-set only consisting of edges going from the source's side to the sink's side.


flow network

(graph theory) A directed graph where each edge has a capacity and each edge receives a flow.


maximum cut

(graph theory) A cut whose size is at least the size of any other cut; a partition of the graph's vertices into two complementary sets S and T, such that the number of edges between S and T is as large as possible.


minimum cut

(graph theory) A cut that is minimal in some metric.


rooted tree

(graph theory) A tree in which one vertex has been designated as the root.


polygon-circle graph

polygon-circle graph (plural polygon-circle graphs)

A common generalization of these two [circle graphs and circular arc graphs] are polygon-circle graphs, intersection graphs of convex polygons inscribed to the circle. This class was first suggested by M. Fellows [personal communication with the first author] in 1988, when it was pointed out that this class of graphs is closed under taking induced minors.

2004, Jan Kratochvíl, Martin Pergel, “Two Results on Intersection Graphs of Polygons”, in Giuseppe Liotta, editor, GD 2003 International Symposium on Graph Drawing (Lecture Notes in Computer Science), volume 2912, Springer-Verlag, →DOI, →ISBN, page 60:

(graph theory) A graph (set of connected points) in which each vertex corresponds to a convex polygon circumscribed in a common circle, and in which (graph) vertices are adjacent iff their corresponding polygons intersect geometrically.


Borůvka's algorithm

(graph theory) A greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is not connected.


Tarjan's algorithm

(graph theory) An algorithm for finding the strongly connected components (SCCs) of a directed (connected) graph by using the depth-first search function.


Heawood conjecture

Formulated in 1890 by Percy John Heawood.

(graph theory) A conjecture (proven in 1968) that gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus.


Heawood graph

(graph theory) An undirected graph with 14 vertices and 21 edges.


outerthickness

(graph theory) The minimum number of outerplanar subgraphs which a given graph can decompose into.


multiflow

For vertex-capacitated multiflows the unary case has to be distinguished from vertex-disjoint paths if G is restricted for instance to planar graphs.

2008, Guyslain Naves, András Sebő, “Multiflow Feasibility: An Annotated Tableau”, in William J. Cook, László Lovász, Jens Vygen, editors, Research Trends in Combinatorial Optimization, Berlin: Springer, →ISBN, page 266:

Given that several dependency types flow through the networks, multicommodity flows or multiflows is a natural theoretical framework to map the presented model for further investigations.

2010, Bernhard Hämmerli, Critical Information Infrastructures Security, page 32:

Despite these restricted multiflows, the gap between integer and half-integer flow is at least 1/2 for these graphs […]

2020, Naveen Garg, Nikhil Kumar, András Sebő, “Integer Plane Multiflow Maximisation: Flow-Cut Gap and One-Quarter-Approximation”, in Daniel Bienstock, Giacomo Zambelli, editors, Integer Programming and Combinatorial Optimization: 21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings (Lecture Notes in Computer Science; 12125), Cham: Springer Nature, →ISBN, page 148:

(graph theory) A flow function that operates on the set of edges (ordered pairs of vertices) on the intersection of two related directed graphs.