Volume :1 , Issue :3 ,Page :118-128

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. A partition of V(G) is called eccentric doma tic if all its classes are eccentric dominating sets in G. The maximum number of classes of an eccent ric domatic partition of V(G) is called the eccentric domatic number of G and is denoted by d ed (G). In this paper, bounds for d ed (G) and its exact value for some particular classes of graphs are studied