• THE NUMBER OF MINIMUM CO – ISOLATED LOCATING DOMINATING SETS OF PATHS

Abstract

Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set   S Í V of a graph G is a dominating set, if every vertex in V – S is adjacent to atleast one vertex in S. A dominating set S Í V is called a locating dominating set, if for any two vertices v, w Î V – S, N(v) Ç S ¹ N(w) Ç S. A locating dominating set S Í V is called a co – isolated locating dominating set, if there exists atleast one  isolated vertex in <V – S >. The co – isolated locating domination number g_cild is the minimum cardinality of a co – isolated locating dominating set.  The number of minimum co – isolated locating dominating sets in a graph G is denoted by g_Dcild(G). In this paper, the number g_Dcild is obtained for a Path P_n, where n 3.