Ramanujan graph

Ramanujan graph (plural Ramanujan graphs)

Named after mathematician Srinivasa Ramanujan.

(graph theory) A regular graph whose spectral gap is almost as large as possible, making it an excellent spectral expander. Such graphs are relevant to diverse branches of pure mathematics.


clustering coefficient

en-noun

clustering coefficient (plural clustering coefficients)

(graph theory) A quantitative measure of how often the nodes of a graph cluster together, defined as the ratio of the number of links among the nodes to the maximum possible number of links.


pebbler

(graph theory) One who or that which places pebbles at the vertex of a graph, according to certain rules; see pebble game.


multihypergraph

From multi- + hypergraph. Compare 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 hyperedge) is a subset of V.


antimedian

(graph theory) A function that maximizes the sum of distances to a set of nodes in a graph.


squaregraph

(graph theory) a type of undirected graph that can be drawn in the plane in such a way that every bounded face is a quadrilateral and every vertex with three or fewer neighbors is incident to an unbounded face.


oriented graph

(graph theory) A directed graph having no opposite pairs of directed edges.


graph homomorphism

graph homomorphism (plural graph homomorphisms)

(graph theory) A mapping between two graphs that respects their structure.


semiconnected

(graph theory) Containing a directed path from u to v or a directed path from v to u for every pair of vertices u, v.


Eulerian path

(graph theory) A walk that uses every edge of a graph exactly once.


Eulerian cycle

Eulerian circuit
Eulerian circuit#English

(graph theory) Synonym of Eulerian circuit


articulation point

articulation point (plural articulation points)

(graph theory) A vertex whose removal would disconnect the graph.


binding number

(graph theory) The smallest possible ratio of the number of neighbours of a proper subset of vertices to the size of the subset.


Kneser graph

Named after Martin Kneser, who first investigated them in 1956.

(graph theory) A graph K(n, k) (alternatively KG_(n,k)), whose vertices correspond to the k-element subsets of a set of n elements, and where two vertices are adjacent iff the two corresponding sets are disjoint.


anti-edge

anti-edges (plural)
antiedge (alternative)

(graph theory) A pair of vertices that do not form an edge.


Meyniel graph

(graph theory) A graph in which every odd cycle of length five or more has at least two chords.


Yao graph

(graph theory) A kind of geometric spanner, a weighted undirected graph connecting a set of geometric points with the property that, for every pair of points in the graph, their shortest path has a length that is within a constant factor of their Euclidean distance.


diamond graph

(graph theory) An undirected graph with four vertices and five edges.


Euler genus

(graph theory) The minimal integer n such that the given graph can be drawn without crossing itself on a sphere with n cross-caps or with n/2 handles.


demigenus

(graph theory) The minimal integer n such that the given graph can be drawn without crossing itself on a sphere with n cross-caps.


achromatic number

achromatic number (plural achromatic numbers)

(graph theory) The largest possible number of colors in any coloring for a given graph.


anti-triangle

(graph theory) A three-vertex independent set, the complement of a triangle.


Eulerian graph

Named after mathematician Leonhard Euler, who studied graphs of this type when solving the Seven Bridges of Königsberg problem.

(graph theory) a graph containing an Eulerian circuit.

Eulerian graph
Leonhard Euler
Seven Bridges of Königsberg


cop number

cop numbers (plural)
copnumber (alternative)

(graph theory) For a given undirected graph, the minimum number of cops that suffices to ensure a win (i.e. a capture of the robber) in a certain pursuit–evasion game on the graph.


Mycielskian

(graph theory) A larger graph formed from a given undirected graph by a particular construction that preserves the property of being triangle-free but increases the chromatic number.


Mycielski graph

Mycielski graph (plural Mycielski graphs)


Grötzsch graph

Named after German mathematician Herbert Grötzsch.

(graph theory) A triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is a member of an infinite sequence of triangle-free graphs, each the Mycielskian of the previous graph in the sequence.


functional graph

functional graph (plural functional graphs)

(graph theory) A directed graph whose every vertex has outdegree 1.


Grötzsch's theorem

Named after German mathematician Herbert Grötzsch, who published a proof in 1959.

(graph theory) The statement that every triangle-free planar graph has a coloring using only three colors.


Frucht's theorem

(graph theory) The statement that every finite group is the group of symmetries of a finite undirected graph. More strongly, for any finite group G there exist infinitely many non-isomorphic simple connected graphs such that the automorphism group of each of them is isomorphic to G.


vertex separation number

vertex separation number (plural vertex separation numbers)


Turán's brick factory problem

Named after Pál Turán, who formulated it while working in a brick factory during World War II.

(graph theory) The problem of finding the minimum number of crossings in a drawing of a complete bipartite graph.


theta graph

(graph theory) The union of three internally disjoint (simple) paths that have the same two distinct end vertices.


windmill graph

From the visual resemblance to the sails of a windmill.

(graph theory) The undirected graph Wd(k,n) constructed for k ≥ 2 and n ≥ 2 by joining n copies of the complete graph Kₖ at a shared universal vertex.


graph minor

Tutte conjectured that all snarks have the Petersen graph as a graph minor.

(graph theory) A graph which can be formed from some specified graph by performing vertex deletions, edge deletions, and edge contractions on the specified graph.


edge contraction

edge contraction (plural edge contractions)

Performing an edge contraction on an edge in a path graph results in a path graph with one fewer vertex.

(graph theory) An operation performed on an edge in a graph which deletes the edge, replaces its endpoints with a single new vertex, and replaces edges incident to either endpoint with an edge incident to the new vertex.