On the Seidel Integral Complete Multipartite Graphs

被引：0

作者：

Sheng-mei LV ^{[1
]}

Liang WEI ^{[2
]}

Hai-xing ZHAO ^{[2
]}

机构：

[1] Department of Mathematics,Qinghai Nationality University

[2] Department of Mathematics,Qinghai Normal University

来源：

Acta Mathematicae Applicatae Sinica | 2012年 / 04期

基金：

中国国家自然科学基金;

关键词：

S-polynomial; S-integral; complete multipartite graphs;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

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.

引用

页码：705 / 710

页数：6