- Splitting Graphs
Journal Title: International Journal for Research in Applied Science and Engineering Technology (IJRASET) - Year 2016, Vol 4, Issue 3
Abstract
Let G(V,E) be a graph. A dominating set is a subset S of V such that every vertex not in S is adjacent to at least one vertex in S. The cardinality of a minimum dominating set is called the domination number, (G). A dominating set with vertices is called a -set. Let denote the number of -sets in G. For a graph G, the splitting graph S(G), is obtained by adding a new vertex v corresponding to each vertex v of G and joining v to all vertices which are adjacent to v in G. Here we introduce a new type of graphs called minimum domination splitting graphs or simply -splitting graphs. Let G be a graph and let S1, S2,…,S be the -sets in G. The -splitting graph, S(G), of a graph G is the graph obtained from G by adding new vertices w1,w2,…,w and joining wi to each vertex in Si where 1 i . In this paper, we establish some results on -splitting graphs.
Authors and Affiliations
Selvam Avadayappan, M. Bhuvaneshwari, R. Iswarya
Keywords
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