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Dominating set

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.

History, Variants & Algorithms and computational complexity

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Formal definition

History

Algorithms and computational complexity

Variants

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Map overview Semantic statistics

Dominating set

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

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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

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Important terminology

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

Entity relationships Subject–Predicate–Object triples

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

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