The eccentricity e(u) of a point or a node u of a graph G is the maximum dis-tance ofuto any other point of G. A point v is an eccentric point of u if the distance from u to v equals e(u). A graph G is called an unique eccentric point(u.e.p) graph if each point of G has a unique eccentric point. On the other hand, the eccentric graph Ge of a graph G is defined as a graph having the same set of points as G with two points u and v being adjacent in Ge if and only if either u is an eccentric point of v in G or vis an eccentric point of u in G. In this paper we obtain some properties of eccentric graphs of certainu.e.p graphs and diameter maximal graphs.
