On the Seidel Integral Complete Multipartite Graphs  

作　　者：Sheng-mei LV Liang WEI Hai-xing ZHAO 

机构地区：[1]Department of Mathematics,Qinghai Nationality University [2]Department of Mathematics,Qinghai Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2012年第4期705-710,共6页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No.60863006);Program for New Century Excellent Talents in University (No.06-0912)

摘　　要：For a simple undirected graph G, denote by λ（G） the （0, 1）-adjacency matrix of G. Let the matrix S（G） = J-I-2A（G） be its Seidel matrix, and let SG（A） = det（AI-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（A） for the complete multipartite graphs G = Kn1,n2,...,n,. A necessary and sufficient condition for the complete tripartite graphs Km,n,t and the complete multipartite graphs Km,.... m,n,...,n to be S-integral is given, respectively.For a simple undirected graph G, denote by λ（G） the （0, 1）-adjacency matrix of G. Let the matrix S（G） = J-I-2A（G） be its Seidel matrix, and let SG（A） = det（AI-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（A） for the complete multipartite graphs G = Kn1,n2,...,n,. A necessary and sufficient condition for the complete tripartite graphs Km,n,t and the complete multipartite graphs Km,.... m,n,...,n to be S-integral is given, respectively.

关 键 词：S-polynomial S-integral complete multipartite graphs 

分 类 号：O157.5[理学—数学] O172.2[理学—基础数学]