亚循环群的幂图的谱性质
Spectral Properties of Power Graphs of Metacyclic Groups
浏览论文内容
中文总结 AI 辅助
本文研究亚循环群的幂图，刻画其结构，推导三类矩阵的特征多项式显式式，得到两类矩阵谱半径的上下界，丰富群幂图的谱性质研究。
中文摘要 AI 辅助
对于群Ω，其对应的幂图P(Ω)定义为以Ω的元素为顶点的图，当Ω中两个不同顶点u、v满足u=vᵐ或v=uⁿ（m、n∈ℕ）时二者相邻。本文完全刻画了亚循环群类对应的幂图的结构，在此结构描述基础上，推导了邻接矩阵、拉普拉斯矩阵、无符号拉普拉斯矩阵的特征多项式显式表达式，还得到了邻接矩阵和无符号拉普拉斯矩阵的谱半径的上下界。
英文摘要
For a group $Ω$, the associated power graph $P(Ω)$ is defined as the graph whose vertices are the elements of $Ω$, with two distinct vertices $u,v\in Ω$ being adjacent if either $u=v^m$ or $v=u^n$ for some $m,n \in \mathbb{N}$. In this paper, we completely characterise the structure of the power graph associated with the class of metacyclic groups. Building on this structural description, we derive explicit expressions for the characteristic polynomials of the adjacency, Laplacian, and signless Laplacian matrices. Moreover, we obtain lower and upper bounds for the spectral radii of the adjacency and signless Laplacian matrices.
