一类p-群的非交换图的谱性质

The Properties of Spectrum of Non-Commuting Graphs of a Class of p-Groups

有限非交换群的非交换图是一类简单无向图,它以群的非中心元为顶点,两顶点相邻接当且仅当它们的乘积不可交换。本文研究了p3阶群的非交换图的相关谱性质,包括邻接谱、拉普拉斯谱,拟拉普拉斯谱以及正规拉普拉斯谱等。

Non-commuting graphs of finite non-abelian groups are a class of simple undirected graphs that take the non-central elements of the group as vertices, and two vertices are adjacent if and only if their product is non commutative. This paper investigates the spectral properties of non-commuting graphs of groups of order p3, including adjacency spectra, Laplace spectra, quasi-Laplace spectra, and normal-Laplace spectra.