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 Gs（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.