精品文档---下载后可任意编辑Abel 群上 Cayley 图的谱的开题报告摘要：Cayley 图是群理论中的基本概念，是一种图形表示方法。在 Cayley 图上定义了与群元素相对应的顶点和边，可以通过图形化地表示群元素的运算，方便了对群的讨论。本文讨论了在 Abel 群上 Cayley 图的谱问题。在给出 Abel 群上 Cayley 图的一般性质及其谱的定义后，论述了其谱的性质及应用。最后，给出了一些具体的例子，阐明了 Abel 群上 Cayley 图的谱的具体计算方法及应用。关键词：Cayley 图；Abel 群；谱；讨论。Abstract：Cayley graph is a basic concept in group theory, which is a graphical representation method. The vertices and edges corresponding to the group elements are defined on the Cayley graph, and the operation of group elements can be graphically represented, which facilitates the study of groups. In this paper, the spectral problem of Cayley graphs on Abel groups is studied. After giving the general properties of Cayley graphs on Abel groups and the definition of their spectra, the properties and applications of their spectra are discussed. Finally, some specific examples are given to illustrate the specific calculation method and application of the spectra of Cayley graphs on Abel groups.Keywords: Cayley graph; Abel group; spectrum; study.
