Abstract
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
to be S-integral is given, respectively.
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Supported by the National Natural Science Foundation of China (No. 60863006) and by Program for New Century Excellent Talents in University (No. 06-0912)
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Lv, Sm., Wei, L. & Zhao, Hx. On the seidel integral complete multipartite graphs. Acta Math. Appl. Sin. Engl. Ser. 28, 705–710 (2012). https://doi.org/10.1007/s10255-012-0126-x
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DOI: https://doi.org/10.1007/s10255-012-0126-x