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 2 V (G) ¡ D is adjacent to some vertex v 2 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 2 (V ¡ D) satis¯es N(u) \ D 6 = 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 ° (G). In this paper, we analyze the locating independent domination number of graph operations.