Abstract
Let D(G)=(dij)nxn denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vj in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In this paper, we investigate distance integral complete r-partite graphs Kp1,p2,...,pr = Ka1?p1,a2?p2,...,as?ps and give a sufficient and necessary condition for Ka1?p1,a2?p2,...,as?ps to be distance integral, from which we construct infinitely many new classes of distance integral graphs with s = 1,2,3,4. Finally, we propose two basic open problems for further study.
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