2~np^m阶群上Cayley图的Hamilton圈分解  

Hamiltonian factorization of 2~n P^m degrees Cayley graphs

作　　者：王艳芳[1] 

机构地区：[1]大连大学信息工程学院,辽宁大连116622

出　　处：《辽宁工程技术大学学报（自然科学版）》2009年第6期1033-1036,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(70572069);辽宁省教育厅高校科研计划基金资助项目(2008Z028)

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。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.

关 键 词：CAYLEY图 HAMILTON圈分解 非Abel群 

分 类 号：O157.5[理学—数学]