Infinitely many pairs of cospectral integral regular graphs

A graph G is called integral if all the eigenvalues of the adjacency matrix A(G) of G are integers. In this paper, the graphs G₄(a, b) and G₅(a, b) with 2a+6b vertices are defined. We give their characteristic polynomials from matrix theory and prove that the (n+2)-regular graphs G₄(n, n+2) and G₅(n, n+2) are a pair of non-isomorphic connected cospectral integral regular graphs for any positive integer n.