完全m部图Km（r）的谱

广东工业大学学报 ›› 2008, Vol. 25 ›› Issue (2): 35-37.

完全m部图K_m（r）的谱

广东工业大学应用数学学院；广东工业大学应用数学学院广东广州510006；广东广州510006；

出版日期:2008-06-01 发布日期:2008-06-01

Spectra of Complete M-Partite Graph

Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 510006

Online:2008-06-01 Published:2008-06-01

摘要/Abstract

摘要： 关于带有参数(n,k,a,c)的强正则图,它的特征值具有如下性质:其中有一个特征值是度数k,它的重数取决于图的连通分支数.另外两个特征值分别是方程x2-(a-c)x-(k-c)=0的两个根为θ、T.其重数mθ、mT满足这样的等式:mθ+mT=n-1、k+mθθ+mTT=0.通过这样的性质,由强正则图可以容易得到它的谱.通过这一方法研究一类完全m部图Km(r)的谱.

关键词: 强正则图；完全m部图Km(r)；谱；非本原图；

Abstract: The eigenvalues of a strongly regular graph with parameters(n,k,a,c),are k and θ,T which are the two roots of the quadratic equation x2-(a-c)x-(k-c)=0.The multiplicities mθ and mT can be determined from the equations mθ+mT=n-1,k+mθθ+mTT=0.And this gives an alternative method of determining its spectra.The complete multipartite graph Km(r) is illustrated.

Key words: strongly regular graph； complete multipartite graph； spectra； imprimitive graph；

袁晓莉；郭大昌； . 完全m部图K_m（r）的谱[J]. 广东工业大学学报, 2008, 25(2): 35-37.

Yuan Xiao-li,Guo Da-chang. Spectra of Complete M-Partite Graph[J]. Journal of Guangdong University of Technology, 2008, 25(2): 35-37.

参考文献

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