Volume :3 , Issue :1 ,Page :1-14

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). Also, S is said to be a distance closed dominating set of G if (i) is distance closed and (ii) S is a dominating set. The critical concept in graphs plays an important role in the study of structural properties of graphs and hence it will be useful to study any communicatio n model. The critical concept of distance closed domination which deals with those graphs that are critical in the sense that their distance closed domination number drops when any missing edge is added. The struct ural properties of k-distance closed domination critical graphs for k ≤ 4 are studied in [13]. In this paper, we analyze the structural properties of k- distance closed domi nation critical graphs for k = 5 and 6.