关于轮网络的一簇猜想  

One Variety Conjectures of Wheel Network

作　　者：师海忠[1] 侯斐斐[1] 马继勇[1] 王国亮[1] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《数学的实践与认识》2013年第10期139-144,共6页Mathematics in Practice and Theory

基　　金：甘肃省自然科学基金(ZS991-A25-017-G)

摘　　要：轮网络是由Cayley图模型设计出来的一种新型互连网络模型.星网络、冒泡排序网络、修正冒泡排序网络可嵌入轮网络.为了揭示它的整体结构,对轮网络提出如下一簇猜想:轮网络是边不交的i个Hamilton圈及2(n-i)-2个完美匹配的并,其中1≤i≤(n-1);并证明了当n=4,5,6,1≤i≤3时,猜想成立.Wheel network is a new interconnection networks designed from Cayley graph model. Star network, bubble sort network and modified bubble-sort network are embeddable to wheel network. In this paper, we will give one variety conjectures to show the structure of wheel network. Conjectures are as follows： For any integer n ≥ 4, wheel network Wn is a union of i edge-disjoint hamiltonian cycles and 2（n - i） - 2 perfect matchings, where 1 〈 i 〈 （n - 1）. We prove that the conjectures are true for n = 4, 5, 6 and 1 ≤ i ≤ 3.

关 键 词：CAYLEY图 对换图 轮网络 猜想 HAMILTON圈 

分 类 号：O157.5[理学—数学]