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For a simple undirected graph G, denote by A(G) the (0,1)-adjacency matrix of G. Let thematrix 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 S G (λ) are integral, then the graph G is called S-integral. In this paper, our main goal is to investigate the eigenvalues of S G (λ) for the complete multipartite graphs G = $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 [Figure not available: see fulltext.] to be S-integral is given, respectively.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Nov 21, 2012
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