New class of integral bipartite graphs with large diameter

Abstract

. In this paper, we construct a new class of integral bipartite graphs (not necessarily trees) with large even diameters. In fact, for every finite set A of positive integers of size k we construct an integral bipartite graph G of diameter 2 k such that the set of positive eigenvalues of G is exactly A . This class of integral bipartite graphs has never found before.