关于有限群的强幂图的谱

On the Spectra of Strong Power Graphs of Finite Groups

中文关键词:  强幂图  循环群  特征多项式  谱

英文关键词:strong power graph  cyclic group  characteristic polynomial  spectrum

中文摘要:

      令$G$是一个阶为$n$的有限群, $G$上的强幂图定义为: 以$G$为顶点集, 对于两个不同的元素$x$和$y$, 如果存在两个不超过$n$的正整数$n_1, n_2$使得$x^{n_1}=y^{n_2}$, 则$x$和$y$ 之间连一条边. 本文给出了$G$上强幂图的距离矩阵和邻接矩阵的特征多项式, 并且计算了其距离谱和邻接谱.

英文摘要:

      Let $G$ be a finite group of order $n$. The strong power graph of $G$ is the undirected graph whose vertex set is $G$ and two distinct vertices $x$ and $y$ are adjacent if $x^{n_1}=y^{n_2}$ for some positive integers $n_1,n_2