Construction of a family of uniform central graphs

摘要

A graph is called a uniform central graph if its central vertices have the same set of eccentric vertices. We show that the conjecture ′if a graph with radius r is uniform central, then its diameter is at least r + [(r + 1)/2]′ is not true by constructing a uniform central graph with any given radius and diameter. This construction can be generalized to obtain a uniform central graph which has a given graph as its center.