Spectra of Complete M-Partite Graph

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更新时间：2026-05-27

关于带有参数(n

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.

The eigenvalues of a strongly regular graph with parameters(n

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.

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