论文标题
一些最小连接的素图的家族的邻接光谱
The Adjacency Spectra of Some Families of Minimally Connected Prime Graphs
论文作者
论文摘要
在有限的群体理论中，研究一组的主要图是过去半个世纪的重要主题。最近，仅以图形理论术语来表征可解决组的主要图。现在，这允许研究这些图，而无需了解组理论背景。在本文中，我们从线性代数角度研究了素数图，并专注于早期在该主题的工作中引入的微小连接的素数类别。作为我们的主要结果，我们确定了邻接矩阵的决定因素以及这些图表的某些重要家族的光谱。
In finite group theory, studying the prime graph of a group has been an important topic for almost the past half-century. Recently, prime graphs of solvable groups have been characterized in graph theoretical terms only. This now allows the study of these graphs without any knowledge of the group theoretical background. In this paper we study prime graphs from a linear algebra angle and focus on the class of minimally connected prime graphs introduced in earlier work on the subject. As our main results, we determine the determinants of the adjacency matrices and the spectra of some important families of these graphs.
