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Moore graph

In graph theory, a Moore graph is a regular graph whose girth (the shortest cycle length) is more than twice its diameter (the distance between the farthest two vertices). If the degree of such a graph is d and its diameter is k, its girth must equal 2k + 1. This is true, for a graph of degree d and diameter k, if and only if its number of vertices (its…

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Examples

Complete graphsCyclesPetersen graphHoffman–Singleton graphOpen problems
12 related topics

Overview

Graph theoryRegular graphGirthCycleDiameter
13 related topics

Bounding vertices by degree and diameter

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1 related topics

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Bounding vertices by degree and diameter

Examples

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Map overview Semantic statistics

Moore graph

Nodes30
Edges29
Triples95
Avg. degree1.93
Density0.066667
Components1

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Moore graph

Top relations

related to References · 58
Moore graph → Alan, Alfréd, American Mathematical Monthly, Azarija, Bibcode, Béla, Cambridge Philosophical Society, Convex Cycles, Cycles Are Extremal Graphs, Dalfó, Development, Faculty, Graduate Texts, Graph Theory, Hoffman, Hungar, IBM Journal, Ito, Its Applications, Jernej
related to Examples · 11
Moore graph → C2n, C5, Damerell, Kn, Moore, Singleton, The, The Hoffman, The Petersen, Therefore, This
related to Moore graphs as cages · 10
Moore graph → At, Choose, Each Moore, In, Instead, Moore, Suppose, Therefore, This, Thus
related to Bounding vertices by degree and diameter · 8
Moore graph → Hoffman, In, Let, Moore, Singleton, Therefore, This, Thus
related to External links · 6
Moore graph → Brouwer, Eric, Haemers, Hoffman-Singleton Theorem, MathWorld, Spectra
is a · 2
Moore graph → cage, regular graph whose girth

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Important terminology

moore graph graphs diameter girth vertices degree number must cycles singleton 2k possible hoffman order tree level doi mr search

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Moore graphis aregular graph whose girth0.90text
Moore graphis acage0.90text
Moore graphrelated to Bounding vertices by degree and diameterLet0.60section
Moore graphrelated to Bounding vertices by degree and diameterThis0.60section
Moore graphrelated to Bounding vertices by degree and diameterIn0.60section
Moore graphrelated to Bounding vertices by degree and diameterThus0.60section
Moore graphrelated to Bounding vertices by degree and diameterHoffman0.60section
Moore graphrelated to Bounding vertices by degree and diameterSingleton0.60section
Moore graphrelated to Bounding vertices by degree and diameterMoore0.60section
Moore graphrelated to Bounding vertices by degree and diameterTherefore0.60section
Moore graphrelated to ExamplesThe Hoffman0.60section
Moore graphrelated to ExamplesSingleton0.60section

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