Volume :1 , Issue :2 ,Page :102-108

Abstract : In a graph G = (V, E), a set D  V is a weak convex dominating(WCD) set if each vertex of V-D is adjacent to at le ast one vertex in D and d (u,v) = d G (u,v) for any two vertices u, v in D. A weak convex domination set D is said to be odd(even) W.C.D set, if for any vertex u  V-D, there exists v  D at odd(even) distance from u. The domination number oc  (G) is the smallest order of a odd weak convex dominating set of G and the domination number ec  (G) is the smallest order of a odd weak convex dominating set of G. In this paper we study the change in the behaviour of even weak convex domination number with respect to addition of edges in the respective graph and also the domatic partition of a graph with respect to even dominating sets of a graph..