Variations of Domination in Graphs
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A subset S of V in a graph G = (V,E) is a dominating set if for every vertex v in V-S, there exists at least one vertex u in S such that v is adjacent to u. The minimum cardinality of a dominating set in G is called the domination number of G. The concepts Superior dominating sub graph, Paired equitable domination and Delta domination are introduced. The introduced domination parameter for some class of graphs like Path, Cycle, Complete graph and Complete bipartite graph are calculated. We deal with different types of dominations like Complementary tree total domination and Complementary tree ...
A subset S of V in a graph G = (V,E) is a dominating set if for every vertex v in V-S, there exists at least one vertex u in S such that v is adjacent to u. The minimum cardinality of a dominating set in G is called the domination number of G. The concepts Superior dominating sub graph, Paired equitable domination and Delta domination are introduced. The introduced domination parameter for some class of graphs like Path, Cycle, Complete graph and Complete bipartite graph are calculated. We deal with different types of dominations like Complementary tree total domination and Complementary tree paired domination. The characterization of these parameters are also discussed. Complementary tree paired domination number of merging of two graphs G1 and G2, a graph G with path Pn and a graph G with Cn are calculated. The relationship between total domination number and complementary tree paired domination number in terms of support vertices and leaves is proved.
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