Volume :3 , Issue :3 ,Page :152-162

Abstract :In a graph G = (V, E), a set D  V is a strong convex set if d (u,v) = d G (u,v) for any two vertices u, v in D and the induced graph consists of all sh ortest path connecting every pair of vertices of D. A strong convex set is called as a stro ng convex dominating (SCD) set if each vertex of V-D is adjacent to at least one vertex in D. The strong convex domination number sc  (G) is the smallest order of a strong convex dominating set of G and the codomination number of G, denoted by sc  ( G ), is the strong convex domination number of it s complement. In this paper, we found various bounds of these parameters and characterized the graphs, for which bounds are attained.