4度Cayley图的Hamilton圈分解的新方法与理论证明  

New method and theoretical confirmation on Hamiltonian decomposition of cayley graphs of degree 4

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：《纯粹数学与应用数学》2010年第3期380-386,共7页Pure and Applied Mathematics

基　　金：省教育厅高校科研计划项目(2008Z028)

摘　　要：给出了"Hamilton圈侧枝循环"等四个定理.它揭示了Abel群上4度Cayley图的Hamilton圈分解的特点及规律.同时,提出了Hamilton圈上"单向通道"的"离合"理论.在此基础上给出了Abel群上4度Cayley图的Hamilton圈分解的新方法-"离合法",此方法具有简明、快捷、分解方案多的特点.另外,Hamilton圈"单向通道"的"离合"理论还为解决6度Cayley图的Hamilton圈分解奠定了理论基础.This paper gives the lateral branch cycling theory of Hamiltonian loop and other their theories.It recovers the characteristics and the rules of Hamilton decomposition of 4-degree Cayley graphs on Abel group.Meanwhile,it brings forward clutch theory on single-directional channel over Hamiltonian loop.Based on the theory,a new method,clutch method,for Hamilton decomposition of 4-degree Cayley graphs on Abel group is presented,which is simpler and easier,and provides more decomposition schemes.Moreover,the clutch theory on single-directional channel over Hamiltonian loop establishes the theoretical basis for the research of Hamilton decomposition of 6-degree Cayley graphs.

关 键 词：CAYLEY图 HAMILTON圈 交换群 

分 类 号：O157.5[理学—数学]