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Hoffman–Singleton graph: Algebraic properties, Construction & Subgraphs and supergraphs

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.…

Language: English [EN]

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Hoffman–Singleton graph topic overview

The analysis highlights Algebraic properties, Construction and Subgraphs and supergraphs as prominent areas in the source structure around Hoffman–Singleton graph.

Related topics: 49
Source areas: 4
Connected nodes: 53
Extracted relationships: 45
Concept neighborhoods: 33
Bridge connections: 53

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Algebraic properties · 21 topics

Construction · 13 topics

Overview · 10 topics

Subgraphs and supergraphs · 5 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

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

Suggested research paths

A focused starting point derived from the topic graph, ranked independently of the source article order.

Start with these areas

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Mathematical Mathematics
Graph theory
Regular Regular graph
Undirected graph
Strongly regular graph
Alan Hoffman Alan Hoffman (mathematician)
Moore graph
Degree Degree (graph theory)
Girth Girth (graph theory)
Cage Cage (graph theory)

Construction

Pentagons Pentagon
Pentagrams Pentagram
Modulo Modular arithmetic
PG(3,2)
Fano plane
Even Even permutation
Permutations Permutation
Lexicographic order
Levi graph
Disjoint Disjoint sets
Odd graph
Higman–Sims graph
Binary operation

Algebraic properties

Automorphism group
Group Group (mathematics)
Order Order of a group
Isomorphic Group isomorphism
Semidirect product
Projective special unitary group
Cyclic group
Frobenius automorphism
Acts Group action
Symmetric graph
Permutation group
Generated Generating set of a group
Stabilizer Stabilizer subgroup
Symmetric group
Alternating group
Maximal subgroups Maximal subgroup
Characteristic polynomial
Integral graph
Spectrum Spectral graph theory
Integers Integer
Independent sets Independent set (graph theory)

Subgraphs and supergraphs

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Hoffman–Singleton graph connects Entity context

The extracted context around Hoffman–Singleton graph shows recurring relationship patterns in the source. For example, Hoffman–Singleton graph → Because, Coxeter, Hoffman, Hoffman Singleton, Hoffman-Singleton, Petersen, Removing, Singleton, Sylvester, Take, The, The Hoffman Singleton, There, Tutte-Coxeter Another extracted example is Hoffman–Singleton graph → As, Frobenius, Hoffman, It, PSU, PΣU, Singleton, The, Therefore. Use these groups to spot repeated connection types before inspecting the individual relationships.

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

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

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

Hoffman–Singleton graph relationships Subject–Predicate–Object triples

TTTA extracted 45 structured relationships around Hoffman–Singleton graph. Examples in this analysis include Hoffman–Singleton graph → Automorphisms → 252,000 (PSU(3,52):2) and Hoffman–Singleton graph → Chromatic index → 7. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Hoffman–Singleton graph	Automorphisms	252,000 (PSU(3,52):2)	1.00	infobox
Hoffman–Singleton graph	Chromatic index	7	1.00	infobox
Hoffman–Singleton graph	Chromatic number	4	1.00	infobox
Hoffman–Singleton graph	Diameter	2	1.00	infobox
Hoffman–Singleton graph	Edges	175	1.00	infobox
Hoffman–Singleton graph	Genus	29	1.00	infobox
Hoffman–Singleton graph	Girth	5	1.00	infobox
Hoffman–Singleton graph	Named after	Alan J. Hoffman Robert R. Singleton	1.00	infobox
Hoffman–Singleton graph	Properties	Strongly regular Symmetric Hamiltonian Integral Cage Moore graph	1.00	infobox
Hoffman–Singleton graph	Radius	2	1.00	infobox
Hoffman–Singleton graph	Vertices	50	1.00	infobox
Hoffman–Singleton graph	is a	7-regular undirected graph with 50 vertices and 175 edges	0.90	text
Hoffman–Singleton graph	is a	group of order 252	0.90	text
Hoffman–Singleton graph	is a	symmetric graph	0.90	text
Hoffman–Singleton graph	is a	integral graph	0.90	text

Related concept clusters Concept neighborhoods

The concept neighborhoods around Hoffman–Singleton graph bring nearby vocabulary together. In this analysis, examples include Singleton, Hoffman and Hoffman-singleton. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

Hoffman–Singleton graph
- Singleton
- Hoffman
- Hoffman-singleton
- Graphs
- Robert
- Therefore
- Moore
- Symmetric
- Group
- Edges
- Vertex
- Displaystyle
hoffman–singleton graph
- Singleton
- Hoffman
- Hoffman-singleton
- Vertices
- Graphs
- Therefore
- Robert
- Two
- Displaystyle
- Alan
- Moore
- Symmetric
graph theory
- Singleton
- Hoffman
- Hoffman-singleton
- Vertices
- Two
- Displaystyle
- Edges
- Graphs
- Moore
- Symmetric
- Therefore
- Also
undirected graph
- Singleton
- Hoffman
- Hoffman-singleton
- Vertices
- Two
- Displaystyle
- Edges
- Graphs
- Moore
- Symmetric
- Therefore
- Also
strongly regular graph
- Parameters
- Strongly
- Singleton
- Hoffman
- Girth
- Properties
- Graphs
- Hoffman-singleton
- Moore
- Symmetric
- Vertices
- Two
alan hoffman
- Singleton
- Properties
- Graphs
- Moore
- Pg
- Robert
- Subgraphs
- Therefore
- Also
- Symmetric
- Group
- Displaystyle
moore graph
- Girth
- Singleton
- Hoffman
- Degree
- Hoffman-singleton
- Parameters
- Properties
- Regular
- Strongly
- Vertices
- Robert
- Symmetric
levi graph
- Singleton
- Hoffman
- Hoffman-singleton
- Vertices
- Two
- Displaystyle
- Edges
- Graphs
- Moore
- Symmetric
- Therefore
- Also

Connections between topic areas Semantic bridges

For Hoffman–Singleton graph, one of the stronger structural bridges in this analysis connects Hoffman–Singleton graph with Algebraic properties. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3

Hoffman–Singleton graph — Algebraic properties · splits 32 ⟂ 22

Hoffman–Singleton graph — Construction · splits 40 ⟂ 14

Hoffman–Singleton graph — Overview · splits 43 ⟂ 11

Hoffman–Singleton graph — Subgraphs and supergraphs · splits 48 ⟂ 6

Map overview Semantic statistics

Hoffman–Singleton graph

Nodes54

Edges53

Triples45

Avg. degree1.96

Density0.037037

Components1

Source & methodology

TTTA analyzes the structure around Hoffman–Singleton graph to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Algebraic properties, Construction & Subgraphs and supergraphs, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Hoffman–Singleton graph · EN edition · Analysis: TopicsToTalkAbout

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