Volume :2 , Issue :3 ,Page :139-149

Abstract : A subset D of V is said to be a chromatic strong dominating set (or csd- set) if D is strong dominating set and ) G ( = >) D (<   . The minimum cardinality of chromatic strong dominating set is called chromatic strong domination number and is denoted by ) G ( c s  . In this paper we initiate a study of this pa rameter and we characterize n = ) G ( c s  , where n is the order of G . Key words: Domination, Strong domination, Chromatic Number.