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Windmill graph: Labeling and colouring, Properties & Special cases

In the mathematical field of graph theory, the windmill graph Wd(k,n) is an undirected graph constructed for k ≥ 2 and n ≥ 2 by joining n copies of the complete graph Kk at a shared universal vertex. That is, it is a 1-clique-sum of these complete graphs.

Language: English [EN]
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Windmill graph topic overview

The analysis highlights Labeling and colouring, Properties and Special cases as prominent areas in the source structure around Windmill graph.

Related topics
17
Source areas
4
Connected nodes
21
Extracted relationships
20
Concept neighborhoods
21
Bridge connections
21

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.

Overview · 6 topics
Labeling and colouring · 5 topics
Properties · 3 topics
Special cases · 3 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.

Chromatic index
n(k − 1)
Chromatic number
k
Diameter
2
Girth
3 if k > 2
Notation
Wd(k,n)
Radius
1

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

Properties

Special cases

Labeling and colouring

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 Windmill graph connects Entity context

The extracted context around Windmill graph shows recurring relationship patterns in the source. For example, Windmill graph → Bermond, In, Its, Kotzig, The, Through, Turgeon, Wd Another extracted example is Windmill graph → By, Fn, Sn, Wd. Use these groups to spot repeated connection types before inspecting the individual relationships.

Windmill graph

Top relations

related to Labeling and colouring · 8
Windmill graph → Bermond, In, Its, Kotzig, The, Through, Turgeon, Wd
related to Special cases · 4
Windmill graph → By, Fn, Sn, Wd
Chromatic index · 1
Windmill graph → n(k − 1)
Chromatic number · 1
Windmill graph → k
Diameter · 1
Windmill graph → 2
Edges · 1
Windmill graph → .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:cent…
Girth · 1
Windmill graph → 3 if k 2
Notation · 1
Windmill graph → Wd(k,n)
Radius · 1
Windmill graph → 1
Vertices · 1
Windmill graph → n(k − 1) + 1

Important terminology

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

Important terminology

wd graph windmill complete graceful graphs chromatic proved vertex vertices edges block nk radius diameter girth number index mathematical 1-clique-sum

Windmill graph relationships Subject–Predicate–Object triples

TTTA extracted 20 structured relationships around Windmill graph. Examples in this analysis include Windmill graph → Chromatic index → n(k − 1) and Windmill graph → Chromatic number → k. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Windmill graphChromatic indexn(k − 1)1.00infobox
Windmill graphChromatic numberk1.00infobox
Windmill graphDiameter21.00infobox
Windmill graphEdges.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:cent…1.00infobox
Windmill graphGirth3 if k > 21.00infobox
Windmill graphNotationWd(k,n)1.00infobox
Windmill graphRadius11.00infobox
Windmill graphVerticesn(k − 1) + 11.00infobox
Windmill graphrelated to Labeling and colouringThe0.60section
Windmill graphrelated to Labeling and colouringIts0.60section
Windmill graphrelated to Labeling and colouringWd0.60section
Windmill graphrelated to Labeling and colouringIn0.60section

Related concept clusters Concept neighborhoods

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

  • Windmill graph
    • Graph
    • Windmill
    • Wd
    • Chromatic
    • Complete
    • Graceful
    • Cases
    • Colouring
    • Constructed
    • Copies
    • Field
    • Gallery
  • windmill graph
    • Graph
    • Windmill
    • Wd
    • Chromatic
    • Complete
    • Graceful
    • Cases
    • Colouring
    • Constructed
    • Copies
    • Field
    • Gallery
  • graph theory
    • Shared
    • Undirected
    • Universal
    • Windmill
    • Vertex
    • Wd
    • Chromatic
    • Complete
    • Cases
    • Colouring
    • Constructed
    • Copies
  • undirected graph
    • Universal
    • Windmill
    • Vertex
    • Wd
    • Chromatic
    • Complete
    • Cases
    • Colouring
    • Constructed
    • Copies
    • Gallery
    • Joining
  • complete graph
    • Windmill
    • Vertex
    • Graphs
    • Wd
    • Chromatic
    • 1-clique-sum
    • Complete
    • Constructed
    • Copies
    • Field
    • Graph
    • Joining
  • block graph
    • Windmill
    • Diameter
    • Edges
    • Girth
    • Nk
    • Radius
    • Vertices
    • Wd
    • Index
    • Number
    • Perfect
    • Chromatic
  • friendship graph
    • Windmill
    • Wd
    • Chromatic
    • Complete
    • Cases
    • Colouring
    • Constructed
    • Copies
    • Gallery
    • Joining
    • Kk
    • Labeling
  • star graph
    • Windmill
    • Wd
    • Chromatic
    • Complete
    • Cases
    • Colouring
    • Constructed
    • Copies
    • Gallery
    • Joining
    • Kk
    • Labeling

Connections between topic areas Semantic bridges

For Windmill graph, one of the stronger structural bridges in this analysis connects Windmill graph with Overview. 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
Windmill graph — Overview · splits 15 ⟂ 7
Windmill graph — Labeling and colouring · splits 16 ⟂ 6
Windmill graph — Properties · splits 18 ⟂ 4
Windmill graph — Special cases · splits 18 ⟂ 4

Map overview Semantic statistics

Windmill graph

Nodes22
Edges21
Triples20
Avg. degree1.91
Density0.090909
Components1

Source & methodology

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

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

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