Some new classes of distance integral graphs constructed from integral graphs

The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D(G). A graph is called distance integral if all of its distance eigenvalues are integers. In this paper, we introduce some new classes of distance integral graphs. In particular, we show that if n, k are integers such that n ⩾ 3k 0, then the bipartite Kneser graph H(n, k) is distance integral. Moreover, we determine the distance spectrum of H(n, k). Also, we show that every distance regular integral graph is distance integral.