Volume :2 , Issue :1 ,Page :47-56

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 every vertex in V-D is adjacent to some vertex in D. Combining the above concepts, a distance closed domi nating set of a graph G is defined as follows: A subset S  V(G) is said to be a distance closed dominatin g (D.C.D) set, if is distance closed and S is a dominating set. In this paper, we define a ne w concept of domination called acyclic distance closed domination (A.D.C.D) and analyze some structural properties of graphs and extremal problems relating to the above concepts.