See algebraic graph theory on Wiktionary
{
"forms": [
{
"form": "algebraic graph theories",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "~",
"head": "algebraic graph theory"
},
"expansion": "algebraic graph theory (countable and uncountable, plural algebraic graph theories)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Graph theory",
"orig": "en:Graph theory",
"parents": [
"Mathematics",
"Visualization",
"Formal sciences",
"Computing",
"Interdisciplinary fields",
"Sciences",
"Technology",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "72 28",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "76 24",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "66 34",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "88 12",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "80 20",
"kind": "other",
"name": "Terms with Armenian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "80 20",
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "79 21",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "81 19",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "85 15",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"text": "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.",
"type": "example"
},
{
"ref": "1979, Béla Bollobás, Graph Theory: An Introductory Course, Springer, page 26:",
"text": "The last section introduces elementary algebraic graph theory which is then applied to electrical networks.",
"type": "quote"
},
{
"ref": "1993, Norman Biggs, Algebraic Graph Theory, 2nd edition, Cambridge University Press, page 38:",
"text": "Several famous results in algebraic graph theory, including one of the oldest, are formulae for the numbers of spanning trees of certain graphs.",
"type": "quote"
},
{
"ref": "2013, Chris Godsil, Gordon F. Royle, Algebraic Graph Theory, Springer, page 77:",
"text": "Graphs with diameter d and girth 2d#x2B;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.",
"type": "quote"
}
],
"glosses": [
"The subbranch of graph theory in which algebraic methods are applied to problems about graphs."
],
"id": "en-algebraic_graph_theory-en-noun-qn7AssE0",
"links": [
[
"mathematics",
"mathematics"
],
[
"graph theory",
"graph theory"
],
[
"algebraic",
"algebraic"
],
[
"graph",
"graph"
]
],
"raw_glosses": [
"(uncountable, mathematics, graph theory) The subbranch of graph theory in which algebraic methods are applied to problems about graphs."
],
"tags": [
"uncountable"
],
"topics": [
"graph-theory",
"mathematics",
"sciences"
]
},
{
"categories": [],
"examples": [
{
"text": "1999, B. Kumar, B. H. V. Topping, Developments in Analysis and Design Using Finite Element Methods, Civil-Comp Press, page 25,\nRecently hybrid methods are proposed by Kaveh [2] and Kaveh et al. [18] which employ graph and algebraic graph theories simultaneously for domain decomposition of FE meshes and their nodal ordering."
},
{
"ref": "2017, Danwei Wang, Baolin Wu, Eng Kee Poh, Satellite Formation Flying, Springer, page 102:",
"text": "[A] decentralized continuous formation keeping approach using local relative measurements is proposed based on algebraic graph theories.",
"type": "quote"
},
{
"text": "2019, Zhi-Hong Guan, Bin Hu, Xuemin (Sherman) Shen, Introduction to Hybrid Intelligent Networks, Springer, page 22,\nMathematical tools such as hybrid dynamical systems, complex networks, differential equations, and algebraic graph theories are introduced for modeling and analyzing the hybrid intelligent networks."
}
],
"glosses": [
"A theory developed by applying algebraic graph theory to a particular problem or application."
],
"id": "en-algebraic_graph_theory-en-noun-JOwqaGmj",
"links": [
[
"theory",
"theory"
]
],
"qualifier": "applied mathematics",
"raw_glosses": [
"(countable, applied mathematics) A theory developed by applying algebraic graph theory to a particular problem or application."
],
"tags": [
"countable"
]
}
],
"translations": [
{
"_dis1": "54 46",
"code": "hy",
"lang": "Armenian",
"roman": "hanrahašvakan grafneri tesutʻyun",
"sense": "branch of graph theory",
"word": "հանրահաշվական գրաֆների տեսություն"
},
{
"_dis1": "54 46",
"code": "fi",
"lang": "Finnish",
"sense": "branch of graph theory",
"word": "algebrallinen verkkoteoria"
},
{
"_dis1": "54 46",
"code": "fr",
"lang": "French",
"sense": "branch of graph theory",
"tags": [
"feminine"
],
"word": "théorie algébrique des graphes"
},
{
"_dis1": "54 46",
"code": "de",
"lang": "German",
"sense": "branch of graph theory",
"tags": [
"feminine"
],
"word": "algebraische Graphentheorie"
},
{
"_dis1": "54 46",
"code": "it",
"lang": "Italian",
"sense": "branch of graph theory",
"tags": [
"feminine"
],
"word": "teoria algebrica dei grafi"
}
],
"wikipedia": [
"algebraic graph theory"
],
"word": "algebraic graph theory"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English uncountable nouns",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Armenian translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Italian translations"
],
"forms": [
{
"form": "algebraic graph theories",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "~",
"head": "algebraic graph theory"
},
"expansion": "algebraic graph theory (countable and uncountable, plural algebraic graph theories)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
"English terms with usage examples",
"English uncountable nouns",
"en:Graph theory",
"en:Mathematics"
],
"examples": [
{
"text": "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.",
"type": "example"
},
{
"ref": "1979, Béla Bollobás, Graph Theory: An Introductory Course, Springer, page 26:",
"text": "The last section introduces elementary algebraic graph theory which is then applied to electrical networks.",
"type": "quote"
},
{
"ref": "1993, Norman Biggs, Algebraic Graph Theory, 2nd edition, Cambridge University Press, page 38:",
"text": "Several famous results in algebraic graph theory, including one of the oldest, are formulae for the numbers of spanning trees of certain graphs.",
"type": "quote"
},
{
"ref": "2013, Chris Godsil, Gordon F. Royle, Algebraic Graph Theory, Springer, page 77:",
"text": "Graphs with diameter d and girth 2d#x2B;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.",
"type": "quote"
}
],
"glosses": [
"The subbranch of graph theory in which algebraic methods are applied to problems about graphs."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"graph theory",
"graph theory"
],
[
"algebraic",
"algebraic"
],
[
"graph",
"graph"
]
],
"raw_glosses": [
"(uncountable, mathematics, graph theory) The subbranch of graph theory in which algebraic methods are applied to problems about graphs."
],
"tags": [
"uncountable"
],
"topics": [
"graph-theory",
"mathematics",
"sciences"
]
},
{
"categories": [
"English countable nouns",
"English terms with quotations"
],
"examples": [
{
"text": "1999, B. Kumar, B. H. V. Topping, Developments in Analysis and Design Using Finite Element Methods, Civil-Comp Press, page 25,\nRecently hybrid methods are proposed by Kaveh [2] and Kaveh et al. [18] which employ graph and algebraic graph theories simultaneously for domain decomposition of FE meshes and their nodal ordering."
},
{
"ref": "2017, Danwei Wang, Baolin Wu, Eng Kee Poh, Satellite Formation Flying, Springer, page 102:",
"text": "[A] decentralized continuous formation keeping approach using local relative measurements is proposed based on algebraic graph theories.",
"type": "quote"
},
{
"text": "2019, Zhi-Hong Guan, Bin Hu, Xuemin (Sherman) Shen, Introduction to Hybrid Intelligent Networks, Springer, page 22,\nMathematical tools such as hybrid dynamical systems, complex networks, differential equations, and algebraic graph theories are introduced for modeling and analyzing the hybrid intelligent networks."
}
],
"glosses": [
"A theory developed by applying algebraic graph theory to a particular problem or application."
],
"links": [
[
"theory",
"theory"
]
],
"qualifier": "applied mathematics",
"raw_glosses": [
"(countable, applied mathematics) A theory developed by applying algebraic graph theory to a particular problem or application."
],
"tags": [
"countable"
]
}
],
"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "hanrahašvakan grafneri tesutʻyun",
"sense": "branch of graph theory",
"word": "հանրահաշվական գրաֆների տեսություն"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "branch of graph theory",
"word": "algebrallinen verkkoteoria"
},
{
"code": "fr",
"lang": "French",
"sense": "branch of graph theory",
"tags": [
"feminine"
],
"word": "théorie algébrique des graphes"
},
{
"code": "de",
"lang": "German",
"sense": "branch of graph theory",
"tags": [
"feminine"
],
"word": "algebraische Graphentheorie"
},
{
"code": "it",
"lang": "Italian",
"sense": "branch of graph theory",
"tags": [
"feminine"
],
"word": "teoria algebrica dei grafi"
}
],
"wikipedia": [
"algebraic graph theory"
],
"word": "algebraic graph theory"
}
Download raw JSONL data for algebraic graph theory meaning in All languages combined (4.5kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.