Volume :7 , Issue :1 ,Page :1-15

Abstract :A set D  V(G) is an eccentric dominating set if D is a dominating set of G and for every v  V  D, there exists at least one eccentric vertex of v in D. The minimum cardinality of eccentric dominating set is called the eccentric domination number and is denoted by  ed (G). In this paper, we have provided some new bounds for  ed (G) and established the relation between  ed (G),  0 (G) and  0 (G). We have also charac terized graphs for which  ed (G) = p  1 and p  2.