图的直接和的Hamilton圈研究  

A Study of Hamilton Cycles in the Direct Sum of a Graph

作　　者：胡延忠[1] 叶波[1,2] 

机构地区：[1]湖北工业大学计算机学院,湖北武汉430068 [2]十堰职业技术学院汽车系,湖北十堰442000

出　　处：《十堰职业技术学院学报》2010年第3期103-106,共4页Journal of Shiyan Technical Institute

摘　　要：本文定义了图的直接和的概念,讨论了图的直接和中Hamilton圈的存在性。当图本身存在Hamilton圈时,它的直接和中的Hamilton圈也存在;设图G是n阶图,如果它的极大Hamilton子圈与Cn-1同构,那么它的直接和存在Hamilton圈;本文还研究了极大Hamilton子圈同构于Cn-2的n阶图并得到了三个充分条件。本文最后用超立方体Q4为例展示了这些命题的应用。This paper defines the direct sum of a graph,and discusses the existence of the Hamilton cycles in the direct sum of a graph.When the graph itself has a Hamilton cycle,the Hamilton cycle also exists in the direct sum of the graph.Let G be a graph of order n,if the maximum Hamilton sub-cycle is isomorphic to the Cn-1,then its direct sum has a Hamilton cycle;it was also studied that the maximum Hamilton sub-cycle is isomorphic to the Cn-2,for a graph of order n,and obtained three sufficient conditions.Finally,the application of these propositions is illustrated with the hypercube Q4 as an example.

关 键 词：HAMILTON圈 直接和 同构图 超立方体 

分 类 号：O157[理学—数学]