中文摘要：

令Γ是一个图,如果Γ的图自同构群Aut（Γ）作用在其弧集上正则,则称图Γ为1-正则图。本文给出具有交换点稳定子群的6度1-正则Cayley图的一个完全分类,证明了在同构意义下具有交换点稳定子群的无核6度1-正则Cayley图只有一个。

英文摘要：

A graph Γ is called 1-regular if Aut（Γ） acts regularly on its arcs.In this paper,a complete characterization for 1-regular 6-valent Cayley graphs with an abelian point stabilizer is presented.It is proved that there exists only one core-free 1-regular 6-valent Cayley graph with an abelian point stabilizer.