余图的赛德尔矩阵的无特征值区间

Eigenvalue-Free Interval for Seidel Matrices of Cographs

中文关键词:  余图  赛德尔矩阵  无特征值区间

英文关键词:cograph  Seidel matrix  eigenvalue-free interval

中文摘要:

      本文研究了余图赛德尔特征值的分布.我们证明了区间$(-1, 1)$不含任何非平凡余图的赛德尔特征值.我们还证明了区间$(-1, 1)$的最优性,即对于任意$\epsilon>0$, 区间$(1,1+\epsilon)$和$(-1-\epsilon,-1)$都包含某个阶数充分大的余图的一个赛德尔特征值.

英文摘要:

      The distribution of Seidel eigenvalues of cographs is investigated in this paper. We prove that there is no Seidel eigenvalue of nontrivial cographs in the interval $(-1, 1)$. We also show the optimality of the interval $(-1,1)$ in the sense that for any $\epsilon>0$ either of the intervals $(1,1+\epsilon)$ and $(-1-\epsilon,-1)$ contains a Seidel eigenvalue of some cograph of order $n$ when $n$ is sufficiently large.