Volume :2 , Issue :2 ,Page :57-65

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 restrained dominating set of G if every vertex in V-D is adjacent to a vertex in D and at least a vertex in V-D. In this paper, we define a new conc ept of domination called distance closed restrained domination (D.C.R.D) and analyze so me structural properties of graphs and extremal problems relating to the above concepts.