On Eccentric Graphs of Unique Eccentric Point Graphs and Diameter Maximal Graphs

Abstract

The eccentricity e(u) of a point or a node u of a graph G is the maximum distance of u to 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 v is an eccentric point of u in G. In this paper we obtain some properties of eccentric graphs of certain u.e.p graphs and
diameter maximal graphs.