Domination in graph theory


Now, any two adjacent vertices and of are enough to dominate because the vertices which are not in in must belong to in. Now, we claim that the pendant vertices in are enough to dominate remaining vertices of. These reductions see below show that an efficient algorithm for the minimum dominating set problem would provide an efficient algorithm for the set cover problem, and vice versa. Graph Theory to appear. Table of Contents Alerts. If S is a connected dominating set, one can form a spanning tree of G in which S forms the set of non-leaf vertices of the tree; conversely, if T is any spanning tree in a graph with more than two vertices, the non-leaf vertices of T form a connected dominating set. If is the graph obtained by duplicating each edge of by an edge then every -set of is a global dominating set of and.
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On domination related concepts in Graph Theory

The number of minimal dominating sets is at most 1. Views Read Edit View history. Laskar, On domination and some related topics in graph theory, Proc. Walikar, On the graphs having unique minimum dominating sets, Abstract No. These reductions see below show that an efficient algorithm for the minimum dominating set problem would provide an efficient algorithm for the set cover problem, and vice versa. Both problems are in fact Log-APX-complete.
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Dominating set - Wikipedia

Harvey, and Ken Kennedy of Rice University describe an algorithm that essentially solves the above data flow equations but uses well engineered data structures to improve performance. By using this site, you agree to the Terms of Use and Privacy Policy. The dominators of a node n are given by the maximal solution to the following data-flow equations:. The number of minimal dominating sets is at most 1.
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Domination in graph theory
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Domination in graph theory
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Dominator (graph theory)

Domination in graph theory



Description: By using this site, you agree to the Terms of Use and Privacy Policy. Terms in graph theory. This is an efficient method of computing control dependence, which is critical to the analysis. Both problems are in fact Log-APX-complete.

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