Title: Dominating and Locating Sets in the Multiplication of a Graph
Abstract: A set S of vertices of a graph G is a dominating set of G if every vertex in V(G)\\S is adjacent to some vertex in S, and S is a total dominating set of G if every vertex of G is adjacent to at least one vertex of S. An ordered set W of vertices of a connected graph G is a locating set for G if distinct vertices have distinct codes with respect to W. In this paper, we study the domination and location in the multiplication of a graph. We find the necessary and sufficient conditions for the dominating and locating sets in the multiplication of a graph to exist. We also determine bounds or the exact domination and location numbers of this graph. Keywords: Dominating Set, Locating Code, Locating Set, Multiplication of Graph, Total Dominating Set