Volume :1 , Issue :3 ,Page :109-117

Abstract :In a graph G=(V,E), a set S  V(G) is a distance closed se t 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, a vertex subset D of V(G) is a dominating set of G if each vert ex in V-D is adjacent to at least one vertex in D. In this paper, we define a new concept of domi nation called distance closed domination (D.C.D) and analyze some structural properties of graphs and extremal problems relating to the above concepts.