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Hoffman–Singleton graph

In the mathematical field of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with parameters (50,7,0,1). It was constructed by Alan Hoffman and Robert Singleton while trying to classify all Moore graphs, and is the highest-order Moore graph known to exist.…

Algebraic properties, Construction & Subgraphs and supergraphs

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Automorphisms
252,000 (PSU(3,52):2)
Chromatic index
7
Chromatic number
4
Diameter
2
Edges
175
Genus
29

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Overview

Construction

Algebraic properties

Subgraphs and supergraphs

Advanced semantic analysis

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Map overview Semantic statistics

Hoffman–Singleton graph

Nodes54
Edges53
Triples45
Avg. degree1.96
Density0.037037
Components1

How this topic connects Entity context

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Hoffman–Singleton graph

Top relations

related to Subgraphs and supergraphs · 14
Hoffman–Singleton graph → Because, Coxeter, Hoffman, Hoffman Singleton, Hoffman-Singleton, Petersen, Removing, Singleton, Sylvester, Take, The, The Hoffman Singleton, There, Tutte-Coxeter
related to Algebraic properties · 9
Hoffman–Singleton graph → As, Frobenius, Hoffman, It, PSU, PΣU, Singleton, The, Therefore
is a · 4
Hoffman–Singleton graph → 7-regular undirected graph with 50 vertices and 175 edges, group of order 252, integral graph, symmetric graph
see also · 4
Hoffman–Singleton graph → Hoffman, McKay, Miller, Singleton
related to Construction · 3
Hoffman–Singleton graph → Here, Hoffman, Singleton
Automorphisms · 1
Hoffman–Singleton graph → 252,000 (PSU(3,52):2)
Chromatic index · 1
Hoffman–Singleton graph → 7
Chromatic number · 1
Hoffman–Singleton graph → 4
Diameter · 1
Hoffman–Singleton graph → 2
Edges · 1
Hoffman–Singleton graph → 175

Important terminology Word statistics

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Important terminology

graph hoffman singleton vertices fano hoffman-singleton displaystyle moore group isomorphic exactly vertex 50 alan robert also edges graphs 15 planes

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hoffman–Singleton graphAutomorphisms252,000 (PSU(3,52):2)1.00infobox
Hoffman–Singleton graphChromatic index71.00infobox
Hoffman–Singleton graphChromatic number41.00infobox
Hoffman–Singleton graphDiameter21.00infobox
Hoffman–Singleton graphEdges1751.00infobox
Hoffman–Singleton graphGenus291.00infobox
Hoffman–Singleton graphGirth51.00infobox
Hoffman–Singleton graphNamed afterAlan J. Hoffman Robert R. Singleton1.00infobox
Hoffman–Singleton graphPropertiesStrongly regular Symmetric Hamiltonian Integral Cage Moore graph1.00infobox
Hoffman–Singleton graphRadius21.00infobox
Hoffman–Singleton graphVertices501.00infobox
Hoffman–Singleton graphis a7-regular undirected graph with 50 vertices and 175 edges0.90text
Hoffman–Singleton graphis agroup of order 2520.90text
Hoffman–Singleton graphis asymmetric graph0.90text
Hoffman–Singleton graphis aintegral graph0.90text

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