中文摘要：

Alspach于1985年对Abel群上Cayley图的Hamilton圈分解提出了著名的A猜想,Bermond（1989）证明了4度Abel群上Cayley图对A猜想成立。为了将其研究领域拓广到非Abel群上,采取了有限群上Cayley图的Hamilton圈分解的新方法—＂Hamilton方＂操作法,Abel群上Cayley图对A猜想成立,进一步证明了阶为23p群所含12个群中有10个群的Cayley图（对给定的生成集合）对A猜想成立;另两个群的Cayley图也可分解为边互不相交的Hamilton圈和一个2—因子的并。结果表明：＂Hamilton方＂操作法,具有简明、快捷的优点,而将A猜想拓广到非Abel群上,将为设计互连网算法提供更多的直观路径。

英文摘要：

In 1985,a famous conjecture A for the factorization of Cayley graphs on Abel group was proposed by Alspach.It had been proved by Bermound（1989）that the conjecture A is true for the 4-degree Cayley graph on Abel group.In order to extend the research area to non-Abel group,a new method called ＂Hamilton method＂ for Hamiltonian factorization of Cayley graphs of finite groups is proposed.Conjecture A is true for the Cayley groups on Abel group.Moreover,conjecture A is true for the Cayley graphs （for given generated set） of 10 groups among the 12 groups of degree 2^ 3p.The Cayley graphs of the other two groups can be decomposed into a union of Hamilton loop and a 2-factor.It concludes that ＂Hamilton method＂ is simple and convenient,and that the extension of conjecture A to non-Abel group provides more paths for designing network algorithms.