Volume :3 , Issue :2 ,Page :67-84

Abstract :In a graph G = (V, E), a set S  V(G) is a distance closed set of G if for each vertex u  S and for each w  V – S, there exists at least one vertex v  S such that d (u, v) = d G (u, w) and S is called a dominating set of G if every vertex in V(G) – D is adjacent to some vertex in S. Also, S is said to be a distance closed dominating set of G if (i) is distance clos ed and (ii) S is a dominating set. The concept of distance closed domination in grap hs is studied in [10] and it is useful in communication networks. In this pa per, we have studied the changi ng and unchanging of distance closed domination number in graphs and this concept is more applicab le in a fault tolerance networks.