Volume :2 , Issue :4 ,Page :150-161

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 stud y any communication model. In this paper, we disc uss the critical concept in 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. Also, we analyze some structural properties of those distance closed domination critical graphs