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Odd graph

In the mathematical field of graph theory, the odd graphs are a family of symmetric graphs defined from certain set systems. They include and generalize the Petersen graph.

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Explore the main themes, entities and connections around Odd graph. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Key facts & relationships

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

Diameter
n − 1 {\displaystyle n-1}
Edges
n ( 2 n − 1 n − 1 ) / 2 {\displaystyle n{\tbinom {2n-1}{n-1}}/2}
Girth
3 for O 2 {\displaystyle O_{2}} 5 for O 3 {\displaystyle O_{3}} 6 otherwise
Notation
On
Properties
Distance-transitive
Vertices
( 2 n − 1 n − 1 ) {\displaystyle {\tbinom {2n-1}{n-1}}}

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Overview

Definition and examples

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Properties

Advanced semantic analysis

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Map overview Semantic statistics

Odd graph

Nodes58
Edges57
Triples63
Avg. degree1.97
Density0.034483
Components1

How this topic connects Entity context

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Odd graph

Top relations

related to Independent sets and vertex coloring · 12
Odd graph → Because, Each, Erdős, Further, If, It, Ko, Let, Rado, That, Then, This
related to Edge coloring · 9
Odd graph → Biggs, By Vizing's, Croam, However, In, Is, Petersen, Sundays, When
related to history · 9
Odd graph → Although, Biggs, Kowalewski, Norman Biggs, Odd, Petersen, The, They, Tony Gardiner
related to Hamiltonicity · 8
Odd graph → As, Biggs, For, Hamiltonian, Lovász, The Petersen, This, When
related to Distance and symmetry · 7
Odd graph → As, Cayley, Every, However, If, Odd, Therefore
related to Definition and examples · 6
Odd graph → KG, Kneser, Petersen, That, The, Two
related to External links · 3
Odd graph → Eric, MathWorld, Weisstein
related to Properties · 3
Odd graph → It, The, Therefore
Diameter · 1
Odd graph → n − 1 {\displaystyle n-1}
Edges · 1
Odd graph → n ( 2 n − 1 n − 1 ) / 2 {\displaystyle n{\tbinom {2n-1}{n-1}}/2}

Important terminology Word statistics

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Important terminology

displaystyle odd graph graphs set vertices 2n-1 sets girth n-1 edge independent petersen diameter cycles number two tbinom edges vertex

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Odd graphDiametern − 1 {\displaystyle n-1}1.00infobox
Odd graphEdgesn ( 2 n − 1 n − 1 ) / 2 {\displaystyle n{\tbinom {2n-1}{n-1}}/2}1.00infobox
Odd graphGirth3 for O 2 {\displaystyle O_{2}} 5 for O 3 {\displaystyle O_{3}} 6 otherwise1.00infobox
Odd graphNotationOn1.00infobox
Odd graphPropertiesDistance-transitive1.00infobox
Odd graphVertices( 2 n − 1 n − 1 ) {\displaystyle {\tbinom {2n-1}{n-1}}}1.00infobox
Odd graphrelated to Definition and examplesThe0.60section
Odd graphrelated to Definition and examplesTwo0.60section
Odd graphrelated to Definition and examplesThat0.60section
Odd graphrelated to Definition and examplesKneser0.60section
Odd graphrelated to Definition and examplesKG0.60section
Odd graphrelated to Definition and examplesPetersen0.60section

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