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Crown graph

In graph theory, a branch of mathematics, a crown graph on 2n vertices is an undirected graph with two sets of vertices {u1, u2, …, un} and {v1, v2, …, vn} and with an edge from ui to vj whenever i ≠ j.

Applications & Measurement

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Research this topic

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

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Key facts & relationships

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

Chromatic number
{ 1 n = 1 2 otherwise {\displaystyle \left\{{\begin{array}{ll}1&n=1\\2&{\text{otherwise}}\end{array}}\right.}
Diameter
{ ∞ n ≤ 2 3 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.}
Edges
n(n − 1)
Girth
{ ∞ n ≤ 2 6 n = 3 4 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\6&n=3\\4&{\text{otherwise}}\end{array}}\right.}
Notation
S n 0 {\displaystyle S_{n}^{0}}
Properties
Distance-transitive

Topics to explore

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Overview

Examples

Properties

Applications

Bibliography

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

Crown graph

Nodes65
Edges64
Triples34
Avg. degree1.97
Density0.030769
Components1

How this topic connects Entity context

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

Crown graph

Top relations

has application · 10
Crown graph → Crown, For, Fürer, Hamiltonian, In, Jn, Johnson, Johnson’s, The, This
related to Properties · 8
Crown graph → An, Archdeacon, Crown, Euclidean, However, Its, The, This
related to Examples · 3
Crown graph → In, Schläfli, The
related to External links · 3
Crown graph → Eric, MathWorld, Weisstein
is a · 2
Crown graph → Cartesian product of complete graphs K2, pronic number n
Chromatic number · 1
Crown graph → { 1 n = 1 2 otherwise {\displaystyle \left\{{\begin{array}{ll}1&n=1\\2&{\text{otherwise}}\end{array}}\right.}
Diameter · 1
Crown graph → { ∞ n ≤ 2 3 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.}
Edges · 1
Crown graph → n(n − 1)
Girth · 1
Crown graph → { ∞ n ≤ 2 6 n = 3 4 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\6&n=3\\4&{\text{otherwise}}\end{array}}\right.}
Notation · 1
Crown graph → S n 0 {\displaystyle S_{n}^{0}}

Important terminology Word statistics

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

Important terminology

crown graph graphs number mr edges doi vertices 10 complete mathematics bipartite one two 2n coloring cycles may unit example

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Crown graphChromatic number{ 1 n = 1 2 otherwise {\displaystyle \left\{{\begin{array}{ll}1&n=1\\2&{\text{otherwise}}\end{array}}\right.}1.00infobox
Crown graphDiameter{ ∞ n ≤ 2 3 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.}1.00infobox
Crown graphEdgesn(n − 1)1.00infobox
Crown graphGirth{ ∞ n ≤ 2 6 n = 3 4 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\6&n=3\\4&{\text{otherwise}}\end{array}}\right.}1.00infobox
Crown graphNotationS n 0 {\displaystyle S_{n}^{0}}1.00infobox
Crown graphPropertiesDistance-transitive1.00infobox
Crown graphRadius{ ∞ n ≤ 2 3 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.}1.00infobox
Crown graphVertices2n1.00infobox
Crown graphis apronic number n0.90text
Crown graphis aCartesian product of complete graphs K20.90text
Crown graphhas applicationIn0.60section
Crown graphhas applicationThe0.60section

Related concept clusters Concept neighborhoods

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    Connections between topic areas Semantic bridges

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    Min side: 3
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