New class of integral bipartite graphs with large diameter

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 ۲k such that the set of positive eigenvalues of G is exactly A‎. ‎This class of integral bipartite graphs has never found before‎.

Keywords:

Integral graph , Diameter , root