Volume :1 , Issue :1 ,Page :43-54

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 least one vertex in D and d (u,v) = d G (u,v) for any two vertices u, v in D. A weak convex dominating set D, whose induced graph has no cycle is called acyclic weak convex dominating (AWCD) set. The domination number ac  (G) is the smallest order of a acyclic weak convex dominating set of G and th e codomination number of G, written ac  ( G ), is the acyclic weak convex domination number of its complement. In this paper we found various bounds for these parameters and characterized the gr aphs which attain these bounds