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Dominating set: History, Variants & Algorithms and computational complexity

In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D. The domination number γ(G) is the number of vertices in a smallest dominating set for G.

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Dominating set topic overview

The analysis highlights History, Variants and Algorithms and computational complexity as prominent areas in the source structure around Dominating set.

Related topics
65
Source areas
5
Connected nodes
70
Extracted relationships
374
Concept neighborhoods
37
Bridge connections
70

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.

Variants · 27 topics
Algorithms and computational complexity · 19 topics
Overview · 16 topics
History · 2 topics
Formal definition · 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

Formal definition

History

Algorithms and computational complexity

Variants

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 Dominating set connects Entity context

The extracted context around Dominating set shows recurring relationship patterns in the source. For example, Dominating set → Abhay, ACM, ACM Transactions, Aharoni, AID-NET4, AKCE International Journal, Alber, Alexey, Algorithms, Allan, Analysis, Analytic Algorithmics, Andreas, Annual ACM Symposium, Annual European Symposium, Applications, Applied Mathematics, Approximability, Approximating Fault-Tolerant Domination, Approximation Another extracted example is Dominating set → Advanced Topics, Algorithmica, Approximation, Cite, CiteSeerX, Discrete Algorithms, Domination, Douglas, Fundamentals, Grandoni, Graph Theory, Graphs, Guha, Haynes, Hedetniemi, Introduction, ISBN, Journal, Khuller, Marcel Dekker. Use these groups to spot repeated connection types before inspecting the individual relationships.

Dominating set

Top relations

related to References · 282
Dominating set → Abhay, ACM, ACM Transactions, Aharoni, AID-NET4, AKCE International Journal, Alber, Alexey, Algorithms, Allan, Analysis, Analytic Algorithmics, Andreas, Annual ACM Symposium, Annual European Symposium, Applications, Applied Mathematics, Approximability, Approximating Fault-Tolerant Domination, Approximation
related to Further reading · 30
Dominating set → Advanced Topics, Algorithmica, Approximation, Cite, CiteSeerX, Discrete Algorithms, Domination, Douglas, Fundamentals, Grandoni, Graph Theory, Graphs, Guha, Haynes, Hedetniemi, Introduction, ISBN, Journal, Khuller, Marcel Dekker
related to Algorithms and computational complexity · 12
Dominating set → Both, Karp's, L-reductions, Log-APX-complete, More, Moreover, NP, NP-complete, NP-hard, The, There, These
is a · 10
Dominating set → dominating set in which every vertex in the set has either zero or at least two neighbours outside the set, dominating set of a graph G, dominating set that is also an independent set, dominating set that is also connected, dynamic version of domination in which a vertex v, set D, set of vertices such that all vertices in the graph, set of vertices such that each vertex in the graph has at least k neighbors in the set, star-dominating set and vice versa, subset D
related to Parameterized complexity · 8
Dominating set → Finding, FPT, In, It, More, NP-hard, On, W-hierarchy
related to Exact algorithms · 7
Dominating set → Dijk, Fomin, Grandoni, Kratsch, Nederlof, Rooij, The
related to Special cases · 7
Dominating set → Also, APX, APX-complete, For, If, PTAS, The
related to history · 5
Dominating set → In, NP-complete, Richard Karp, The, This
related to Variants · 5
Dominating set → An, Dominating, Equality, Since, The
related to Formal definition · 3
Dominating set → Every, Given, The

Important terminology

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

Important terminology

dominating set graph doi displaystyle domination 10 graphs minimum vertices problem sets vertex number gamma cover also isbn every 1016

Dominating set relationships Subject–Predicate–Object triples

TTTA extracted 374 structured relationships around Dominating set. Examples in this analysis include Dominating set → is a → dominating set that is also an independent set and Dominating set → is a → dominating set that is also connected. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Dominating setis adominating set that is also an independent set0.90text
Dominating setis adominating set that is also connected0.90text
Dominating setis aset of vertices such that all vertices in the graph0.90text
Dominating setis aset D0.90text
Dominating setis aset of vertices such that each vertex in the graph has at least k neighbors in the set0.90text
Dominating setis asubset D0.90text
Dominating setis astar-dominating set and vice versa0.90text
Dominating setis adynamic version of domination in which a vertex v0.90text
Dominating setis adominating set of a graph G0.90text
Dominating setis adominating set in which every vertex in the set has either zero or at least two neighbours outside the set0.90text
unit disk graphsinstance offor special cases0.80text
planar graphsinstance offor special cases0.80text

Related concept clusters Concept neighborhoods

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

  • Dominating set
    • Set
    • Minimum
    • Sets
    • Graph
    • Displaystyle
    • Vertices
    • Vertex
    • Number
    • Problem
    • Every
    • Cover
    • Graphs
  • dominating set
    • Set
    • Minimum
    • Displaystyle
    • Sets
    • Graph
    • Vertex
    • Cover
    • Problem
    • Vertices
    • Every
    • Number
    • One
  • graph theory
    • Vertices
    • Set
    • Dominating
    • Displaystyle
    • Vertex
    • One
    • Also
    • Every
    • Independent
    • Domination
    • Minimum
    • Gamma
  • graph
    • Vertices
    • Set
    • Dominating
    • Displaystyle
    • Vertex
    • One
    • Also
    • Every
    • Independent
    • Domination
    • Minimum
    • Gamma
  • approximation algorithms
    • S2cid
    • Algorithms
    • Approximation
    • Doi
    • Graphs
    • Sets
    • Journal
    • Also
    • Minimum
    • Dominating
    • Graph
    • Problem
  • independent set
    • Minimum
    • Displaystyle
    • Vertex
    • Cover
    • Problem
    • Vertices
    • Every
    • One
    • Also
    • Number
    • Least
    • Size
  • maximal independent set
    • Minimum
    • Displaystyle
    • Vertex
    • Cover
    • Problem
    • Vertices
    • Every
    • One
    • Also
    • Number
    • Least
    • Size
  • split graph
    • Vertices
    • Set
    • Dominating
    • Displaystyle
    • Vertex
    • One
    • Also
    • Every
    • Independent
    • Domination
    • Minimum
    • Gamma

Connections between topic areas Semantic bridges

For Dominating set, one of the stronger structural bridges in this analysis connects Dominating set with Variants. 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
Dominating setVariants · splits 43 ⟂ 28
Dominating setAlgorithms and computational complexity · splits 51 ⟂ 20
Dominating setOverview · splits 54 ⟂ 17
Dominating setHistory · splits 68 ⟂ 3

Map overview Semantic statistics

Dominating set

Nodes71
Edges70
Triples374
Avg. degree1.97
Density0.028169
Components1

Source & methodology

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

Source: Wikipedia — Dominating set · EN edition · Analysis: TopicsToTalkAbout

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