On the Seidel Integral Complete Multipartite Graphs

For a simple undirected graph G,denote by A(G) the(0,1)-adjacency matrix of G.Let the matrix S(G) = J-I-2A(G) be its Seidel matrix,and let S G(λ) = det(λI-S(G)) be its Seidel characteristic polynomial,where I is an identity matrix and J is a square matrix all of whose entries are equal to 1.If all eigenvalues of SG(λ) are integral,then the graph G is called S-integral.In this paper,our main goal is to investigate the eigenvalues of SG(λ) for the complete multipartite graphs G = K n 1,n 2,...,n t.A necessary and sufficient condition for the complete tripartite graphs K m,n,t and the complete multipartite graphs Km,...,m s,n,...,n t to be S-integral is given,respectively.