Volume :1 , Issue :1 ,Page :1-13

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 is called as a weak convex domi nating (WCD) set if each vertex of V-D is adjacent to at least one vertex in D. The weak convex domination number wc ? (G) is the smallest order of a weak convex dominating set of G and the codomination numb er of G, denoted by wc ? ( G ), is the weak convex domination number of its complement. In this paper, we found various bounds of these parameters and characterized the graphs, for which bounds are attained.