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On the seidel integral complete multipartite graphs

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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

On the seidel integral complete multipartite graphs

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0126-x
Publisher site
See Article on Publisher Site

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 [Figure not available: see fulltext.] to be S-integral is given, respectively.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 21, 2012

References