Independent Domination Number of Operation Graph

Abstract

Let G be a simple, undirected and connected graph. An independent set or stable set is a set of vertices in a graph in which no two of vertices are adjacent. A set D of vertices of graph G is called a dominating set if every vertex u ∈ V (G) − D is adjacent to some vertex v ∈ D. A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. A minimum independent dominating set is an independent set of smallest possible size for a given graph G. This size is called the independence number of G, and denoted i(G). Operation Graph is a technical to get a new graph types by performing the operation of two or more graphs. Power Graph is a operation graph where let the graph G and H , notation of the power graph is (GH ). Keywords: r-dynamic coloring, r-dynamic chromatic number, graph operations.