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Efficient dominating set: History & Applications

In graph theory, an efficient dominating set (also called an e.d. set or independent perfect dominating set) is a dominating set with the additional property that every vertex in the graph is dominated by exactly one vertex in the set.

Language: English [EN]
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Efficient dominating set topic overview

The analysis highlights History and Applications as prominent areas in the source structure around Efficient dominating set.

Related topics
34
Source areas
6
Connected nodes
40
Extracted relationships
22
Concept neighborhoods
29
Bridge connections
40

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.

Complexity · 9 topics
History and applications · 9 topics
Examples · 6 topics
Overview · 6 topics
Definition · 3 topics
Related 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.

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

Definition

Complexity

Examples

History and applications

Related problems

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 Efficient dominating set connects Entity context

The extracted context around Efficient dominating set shows recurring relationship patterns in the source. For example, Efficient dominating set → Bange, Barkauskas, Biggs's, Efficient, I/O, Later, Norman Biggs, Slater, The, When Another extracted example is Efficient dominating set → An, EED, Formally, The, The EED, Unlike. Use these groups to spot repeated connection types before inspecting the individual relationships.

Efficient dominating set

Top relations

related to history · 10
Efficient dominating set → Bange, Barkauskas, Biggs's, Efficient, I/O, Later, Norman Biggs, Slater, The, When
related to Related problems · 6
Efficient dominating set → An, EED, Formally, The, The EED, Unlike
related to Examples · 3
Efficient dominating set → Sierpiński, The, These
related to Definition · 2
Efficient dominating set → An, More
is a · 1
Efficient dominating set → variant where domination is restricted to neighbors of equal or higher degree

Important terminology

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

Important terminology

dominating efficient set displaystyle graph graphs every vertex sets one problem exactly domination concept perfect circulant distance restricted np-complete applications

Efficient dominating set relationships Subject–Predicate–Object triples

TTTA extracted 22 structured relationships around Efficient dominating set. Examples in this analysis include Efficient dominating set → is a → variant where domination is restricted to neighbors of equal or higher degree and Efficient dominating set → related to Definition → An. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Efficient dominating setis avariant where domination is restricted to neighbors of equal or higher degree0.90text
Efficient dominating setrelated to DefinitionAn0.60section
Efficient dominating setrelated to DefinitionMore0.60section
Efficient dominating setrelated to ExamplesSierpiński0.60section
Efficient dominating setrelated to ExamplesThese0.60section
Efficient dominating setrelated to ExamplesThe0.60section
Efficient dominating setrelated to historyThe0.60section
Efficient dominating setrelated to historyNorman Biggs0.60section
Efficient dominating setrelated to historyLater0.60section
Efficient dominating setrelated to historyBiggs's0.60section
Efficient dominating setrelated to historyBange0.60section
Efficient dominating setrelated to historyBarkauskas0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Efficient dominating set bring nearby vocabulary together. In this analysis, examples include Dominating, Efficient and Set. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Efficient dominating set
    • Dominating
    • Efficient
    • Set
    • Displaystyle
    • Sets
    • Every
    • Graph
    • Graphs
    • Domination
    • Exactly
    • One
    • Vertex
  • efficient dominating set
    • Dominating
    • Efficient
    • Set
    • Displaystyle
    • One
    • Vertex
    • Every
    • Sets
    • Graph
    • Exactly
    • Graphs
    • Domination
  • graph theory
    • Displaystyle
    • Every
    • Set
    • One
    • Dominating
    • Vertex
    • Efficient
    • Exactly
    • Problem
    • Examples
    • Given
    • Chordal
  • dominating set
    • Efficient
    • Set
    • Displaystyle
    • One
    • Vertex
    • Every
    • Sets
    • Graph
    • Exactly
    • Graphs
    • Closed
    • Subseteq
  • graph
    • Displaystyle
    • Every
    • Set
    • One
    • Dominating
    • Vertex
    • Efficient
    • Exactly
    • Problem
    • Examples
    • Given
    • Chordal
  • minimum dominating set
    • Efficient
    • Set
    • Displaystyle
    • One
    • Vertex
    • Every
    • Sets
    • Graph
    • Exactly
    • Graphs
    • Closed
    • Subseteq
  • chordal graphs
    • Linear
    • Time
    • Problem
    • Examples
    • Chordal
    • Graphs
    • Np-complete
    • Restricted
    • Circulant
    • Displaystyle
    • Sets
    • 3-regular
  • chordal bipartite graphs
    • Linear
    • Time
    • Problem
    • Examples
    • Chordal
    • Graphs
    • Np-complete
    • Restricted
    • Circulant
    • Displaystyle
    • Sets
    • 3-regular

Connections between topic areas Semantic bridges

For Efficient dominating set, one of the stronger structural bridges in this analysis connects Efficient dominating set with Complexity. 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
Efficient dominating setComplexity · splits 31 ⟂ 10
Efficient dominating setHistory and applications · splits 31 ⟂ 10
Efficient dominating setOverview · splits 34 ⟂ 7
Efficient dominating setExamples · splits 34 ⟂ 7
Efficient dominating setDefinition · splits 37 ⟂ 4

Map overview Semantic statistics

Efficient dominating set

Nodes41
Edges40
Triples22
Avg. degree1.95
Density0.04878
Components1

Source & methodology

TTTA analyzes the structure around Efficient dominating set to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History & Applications, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Efficient dominating set · EN edition · Analysis: TopicsToTalkAbout

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