# Domination in graph theory

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## The Forced Domination Number Of A Graph

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### Isolate domination in graphs

This proved the dominating set problem to be NP-complete as well. An independent set in L G corresponds to a matching in G , and a dominating set in L G corresponds to an edge dominating set in G. In , Richard Karp proved the set cover problem to be NP-complete. It is the most well-known problem complete for the class W[2] and used in many reductions to show intractability of other problems. However, even if the graph admits k-tuple dominating set, a minimum k -tuple dominating set can be nearly k times as large as a minimum k -dominating set for the same graph. [18] An 1. The domatic number is the maximum size of a domatic partition. A minimum dominating set of an n -vertex graph can be found in time O 2 n n by inspecting all vertex subsets. Views Read Edit View history. Conversely, let D be a dominating set for G. From Wikipedia, the free encyclopedia.

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*The domination number of this graph is 2. A k-tuple dominating set is a set of vertices such that each vertex in the graph has at least k neighbors in the set. That is, G is a split graph. Graph theory objects NP-complete problems Computational problems in graph theory. I is a clique and U is an independent set. Dominating sets are closely related to independent sets. In other projects Wikimedia Commons. Moreover, the reductions preserve the approximation ratio. For Dominator in control flow graphs, see Dominator graph theory. The following two reductions show that the minimum dominating set problem and the set cover problem are equivalent under L-reductions. Vizing's conjecture relates the domination number of a cartesian product of graphs to the domination number of its factors. There exist a pair of polynomial-time L-reductions between the minimum dominating set problem and the set cover problem. In each example, each white vertex is adjacent to at least one red vertex, and it is said that the white vertex is dominated by the red vertex.*