完全m部图K_(m(r))的谱

Spectra of Complete M-Partite Graph

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.

The eigenvalues of a strongly regular graph with parameters （n, k, a, c）, are k and O, T which are the two roots of the quadratic equation x^2 - （ a - c） x - （ k - c） = 0. The multiplicities mo and mT can be determined from the equations mo ＋ mT = n - 1, k ＋ mθθ ＋ mTT = 0. And this gives an alternative method of deteivaining its spectra. The complete multipartite graph Km（r） is illustrated.