Johnson graph

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

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Graph-theoretic properties

Isomorphic Hamilton-connected Hamiltonian path Hamiltonian cycle Vertex-edge graph

15 related topics

Special cases

Complete graph Octahedral graph Complement Petersen graph Line graph

6 related topics

Johnson scheme

Association scheme Symmetric difference Shortest path Odd graphs Disjoint

5 related topics

Automorphism group

Distance-transitive Subgroup Isomorphic

3 related topics

Key facts & relationships

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

Diameter: min ( k , n − k ) {\displaystyle \min(k,n-k)}
Edges: 1 2 k ( n − k ) ( n k ) {\displaystyle {\frac {1}{2}}k(n-k){\binom {n}{k}}}
Named after: Selmer M. Johnson
Notation: J ( n , k ) {\displaystyle J(n,k)}
Properties: k ( n − k ) {\displaystyle k(n-k)} -regular Vertex-transitive Distance-transitive Hamilton-connected Polytopal
Vertices: ( n k ) {\displaystyle {\binom {n}{k}}}

Topics to explore

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Overview

Mathematics
Undirected graphs Undirected graph
Subsets Subset
Intersection Intersection (set theory)
Johnson scheme
Selmer M. Johnson

Special cases

Graph-theoretic properties

Automorphism group

Distance-transitive Distance-transitive graph
Subgroup
Isomorphic Group isomorphism

Intersection array

Distance-regular Distance-regular graph
Diameter Diameter (graph theory)

Eigenvalues and eigenvectors

Eigenvectors Eigenvector

Johnson scheme

Open problems

Open problem

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.

Map overview Semantic statistics

Nodes48

Edges47

Triples36

Avg. degree1.96

Density0.041667

Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Johnson graph

Top relations

related to Graph-theoretic properties · 11

Johnson graph → Any, Each Johnson, For, Hamilton-connected, Hamiltonian, In, It, Johnson, More, N-k, The

related to Special cases · 7

Johnson graph → Both, Johnson, K5, Kn, Kneser, More, Petersen

related to External links · 5

Johnson graph → Andries, Eric, Johnson, MathWorldBrouwer, Weisstein

related to Open problems · 4

Johnson graph → However, In, Johnson, The

related to Johnson scheme · 2

Johnson graph → Johnson, The Johnson

Diameter · 1

Johnson graph → min ( k , n − k ) {\displaystyle \min(k,n-k)}

Edges · 1

Johnson graph → 1 2 k ( n − k ) ( n k ) {\displaystyle {\frac {1}{2}}k(n-k){\binom {n}{k}}}

Named after · 1

Johnson graph → Selmer M. Johnson

Notation · 1

Johnson graph → J ( n , k ) {\displaystyle J(n,k)}

Properties · 1

Johnson graph → k ( n − k ) {\displaystyle k(n-k)} -regular Vertex-transitive Distance-transitive Hamilton-connected Polytopal

Important terminology Word statistics

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

Important terminology

displaystyle johnson graph graphs vertices scheme sets distance-transitive n-k number selmer intersection also properties pair given -element set related special

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Johnson graph	Diameter	min ( k , n − k ) {\displaystyle \min(k,n-k)}	1.00	infobox
Johnson graph	Edges	1 2 k ( n − k ) ( n k ) {\displaystyle {\frac {1}{2}}k(n-k){\binom {n}{k}}}	1.00	infobox
Johnson graph	Named after	Selmer M. Johnson	1.00	infobox
Johnson graph	Notation	J ( n , k ) {\displaystyle J(n,k)}	1.00	infobox
Johnson graph	Properties	k ( n − k ) {\displaystyle k(n-k)} -regular Vertex-transitive Distance-transitive Hamilton-connected Polytopal	1.00	infobox
Johnson graph	Vertices	( n k ) {\displaystyle {\binom {n}{k}}}	1.00	infobox
Johnson graph	is a	open problem	0.90	text
Johnson graph	related to External links	Weisstein	0.60	section
Johnson graph	related to External links	Eric	0.60	section
Johnson graph	related to External links	MathWorldBrouwer	0.60	section
Johnson graph	related to External links	Andries	0.60	section
Johnson graph	related to External links	Johnson	0.60	section

Related concept clusters Concept neighborhoods

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Connections between topic areas Semantic bridges

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