Let D（G） =(d_ij)_n×n denote the distance matrix of a connected graph G with order n, where d_ij is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete r-partite graphs K_{p1,p2,···,pr}=K_{a1·p1,a2·p2,···,as···ps} to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs K_{a1·p1,a2·p2,···,as·ps} with s > 4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs K_{a1·p1,a2·p2,···,as·ps} with s = 5, 6. The problem of the existence of such distance integral graphs K_{a1·p1,a2·p2,···,as·ps} with arbitrarily large number s remains open. 

Let D（G） =(d_ij)_n×n denote the distance matrix of a connected graph G with order n, where d_ij is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete r-partite graphs K_{p1,p2,···,pr}=K_{a1·p1,a2·p2,···,as···ps} to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs K_{a1·p1,a2·p2,···,as·ps} with s > 4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs K_{a1·p1,a2·p2,···,as·ps} with s = 5, 6. The problem of the existence of such distance integral graphs K_{a1·p1,a2·p2,···,as·ps} with arbitrarily large number s remains open.