Volume :6 , Issue :1 ,Page :17-27

Abstract :Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set S  V of a graph G is a dominating set, if every vertex in V – S is adjacent to at le ast one vertex in S. A dominating set S  V is called a locating dominating se t, if for any two vertices v, w  V–S, N(v)  S  N(w)  S. A locating dominating set S  V is called a co-isolated locating dominatin g set, if there exists at least one isolated vertex in . The co -isolated locating domination number cild  is the minimum cardinality of a co-isolated locating dominating set. In this paper, upper bounds of co-isolated locating domination number for the Cartesian product of two graphs namely, P 2 ൈ P n (n ≥ 3), P 3 ൈ P n (n ≥ 2),P 4 ൈ P n (n ≥ 2), , P 2 ൈ C n, (n ≥ 3), P 3 ൈ C n, (n≥3), P 4 ൈ C n (n≥3), P 2 ൈ K n, (n ≥ 2), P 3 ൈ K n, (n ≥ 2), P 4 ൈ K n, (n ≥ 3) and K n ൈ K m, (m, n ≥ 3), are established