Volume :5 , Issue :1 ,Page : 24-36

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 subset D of V(G) is a restrained dominating set, if every vertex not in D is adjacent to a vertex in D and to a vertex in V  D. A subset D of V(G) is a restrained eccentric dominating set, if D is a restrained dominating set of G and for every v  V  D, there exists at least one eccentric point of v in D. The minimum of the cardinalities of the restrained eccentric dominating set of G is called the restrain ed eccentric domination number of G and it is denoted by  red (G). In this paper, bounds for  red and its exact value for some particular classes of graphs are found.