关于弧传递Cayley图的判定

On Criterion of Arc-Transitive Cayley Graphs

1938年R. Fruchet证明了对于任意给定的抽象群,都存在一个图以它为自同构群。自此,关于利用群来研究图这一领域,揭开了帷幕。但是,这个领域的广泛研究则是从1960年才真正开始的,尤其是最近30年,在这方面完成了很多重要的工作。本文主要研究了图论的一个分支,即:Cayley图以及它的判定,尤其是弧传递Cayley图的判定。首先,通过研究图的性质以及群的交换性,从而得出本文的主要定理。其次,根据正规弧传递Cayley图的定义以及主要结论的推导过程,得出了一个关于正规弧传递Cayley图的判定条件。

In 1938, R. Fruchet proved that for any given abstract group, there is a graph of it as an automorphism group. Since then, this area, which is about using the groups to study the graphs, opened the curtain. However, extensive research in this area began in 1960, especially in the last 30 years, where a number of important tasks were done. In this paper, we study a branch of graph theory that is, Cayley graph and its decision, especially the arc transitive graph. Firstly, by studying the properties of graph and the exchange of group, we get the main theorem of this paper. Secondly, according to the definition of the normal arc transitive graph and the pushing process of the main conclusion, a judgment condition of the normal arc transitive graph is given.