Volume :2 , Issue :1 ,Page :1-10

Abstract : In a graph G = (V, E), a set D  V is a weak convex set if d (u,v) = d G (u,v) for any two vertices u, v in D. A weak convex set D is called as a weak convex dominating (WCD) set if each vertex of V-D is adjacent to at least one vertex in D. A weak convex dominating set D is called weak convex restrained dominating(WCRD) set if every vertex in V(G)-D is adjac ent to a vertex in D and another vertex in V(G)-D. The domination number ) G ( rc  is the smallest order of a weak convex restrained dominating set of G and the codo mination number of G, written ) G ( rc  , is the weak convex restrained domination number of its complement. In this paper we found various bounds for these parameters and characterized the graphs which attain these bounds.