Volume :1 , Issue :2 ,Page :55-70

Abstract :A subset D of the vertex set V(G) of a graph G is said to be a dominating set if every vertex not in D is adjacent to at least one vertex in D. A dominating set D is said to be an eccentric dominating set if for every v  V  D, there exists at least one eccent ric point of v in D. The minimum of the cardinalities of the eccentric dominating se ts of G is called the eccentric domination number  ed (G) of G. In this paper, bounds for  ed , its exact value for some particular classes of graphs are found.