Unique eccentric point graphs

A graph G is defined to be a unique eccentric point graph (a u.e.p. graph) if each point of G has a unique maximum distance point. Here u.e.p. graphs which are self-centered are characterized. Two construction procedures are given for generating families of u.e.p. graphs from known u.e.p. graphs. Furthermore, some special classes of u.e.p. graphs are studied in detail. © 1983.