Johnson graph

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Johnson graph topic overview

The analysis highlights Graph-theoretic properties, Special cases and Johnson scheme as prominent areas in the source structure around Johnson graph.

Related topics: 39
Source areas: 8
Connected nodes: 47
Extracted relationships: 36
Concept neighborhoods: 35
Bridge connections: 47

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.

Graph-theoretic properties · 15 topics

Overview · 6 topics

Special cases · 6 topics

Johnson scheme · 5 topics

Automorphism group · 3 topics

Intersection array · 2 topics

Eigenvalues and eigenvectors · 1 topics

Open problems · 1 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.

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}}}

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

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.

How Johnson graph connects Entity context

The extracted context around Johnson graph shows recurring relationship patterns in the source. For example, Johnson graph → Any, Each Johnson, For, Hamilton-connected, Hamiltonian, In, It, Johnson, More, N-k, The Another extracted example is Johnson graph → Both, Johnson, K5, Kn, Kneser, More, Petersen. Use these groups to spot repeated connection types before inspecting the individual relationships.

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

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

Johnson graph relationships Subject–Predicate–Object triples

TTTA extracted 36 structured relationships around Johnson graph. Examples in this analysis include Johnson graph → Diameter → min ( k , n − k ) {\displaystyle \min(k,n-k)} and Johnson graph → Edges → 1 2 k ( n − k ) ( n k ) {\displaystyle {\frac {1}{2}}k(n-k){\binom {n}{k}}}. The table shows each extracted connection, where it came from and its confidence.

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

The concept neighborhoods around Johnson graph bring nearby vocabulary together. In this analysis, examples include Graph, Johnson and Graphs. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

Johnson graph
- Graph
- Johnson
- Graphs
- Displaystyle
- Scheme
- Vertices
- N-k
- Sets
- Intersection
- Properties
- Related
- Selmer
johnson graph
- Graph
- Johnson
- Displaystyle
- Graphs
- Scheme
- Pair
- Vertices
- N-k
- Sets
- Intersection
- Number
- Properties
undirected graphs
- Johnson
- Diameter
- Edges
- Vertices
- Properties
- Related
- Distance-transitive
- Given
- Scheme
- Sets
- Graph
- Mathematics
johnson scheme
- Graph
- Graphs
- Selmer
- Displaystyle
- Also
- Pair
- Scheme
- Sets
- Vertices
- N-k
- Array
- Edges
selmer m. johnson
- Graph
- Graphs
- Displaystyle
- Scheme
- Special
- Vertices
- N-k
- Sets
- Intersection
- Properties
- Related
- Selmer
complete graph
- Johnson
- Displaystyle
- Pair
- N-k
- Vertices
- Intersection
- Number
- Scheme
- Graphs
- Array
- Complement
- Diameter
octahedral graph
- Johnson
- Displaystyle
- Pair
- N-k
- Vertices
- Intersection
- Number
- Scheme
- Graphs
- Array
- Complement
- Diameter
petersen graph
- Johnson
- Displaystyle
- Pair
- N-k
- Vertices
- Intersection
- Number
- Scheme
- Graphs
- Array
- Complement
- Diameter

Connections between topic areas Semantic bridges

For Johnson graph, one of the stronger structural bridges in this analysis connects Johnson graph with Graph-theoretic 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

Johnson graph — Graph-theoretic properties · splits 32 ⟂ 16

Johnson graph — Overview · splits 41 ⟂ 7

Johnson graph — Special cases · splits 41 ⟂ 7

Johnson graph — Johnson scheme · splits 42 ⟂ 6

Johnson graph — Automorphism group · splits 44 ⟂ 4

Johnson graph — Intersection array · splits 45 ⟂ 3

Map overview Semantic statistics

Johnson graph

Nodes48

Edges47

Triples36

Avg. degree1.96

Density0.041667

Components1

Source & methodology

TTTA analyzes the structure around Johnson graph to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Graph-theoretic properties, Special cases & Johnson scheme, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Johnson graph · EN edition · Analysis: TopicsToTalkAbout