On locating independent domination number of amalgamation graphs

Abstract

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 D is an independent set and every vertex not in D is adjacent to a vertex in D. By locating independent dominating set of graph G, we mean that an independent dominating set D of G with the additional properties that for u,v (V - D) satisfies N(u) ∩ D ≠ N (v) ∩ D. A minimum locating independent dominating set is a locating independent dominating set of smallest possible size for a given graph G. This size is called the locating independent dominating number of G and denoted γ Li(G). In this paper, we analyze the locating independent domination number of graph operations.