关于紧优双环网络的无限族  

On Infinite Family of Tight Optimal Double Loop Networks

作　　者：徐喜荣[1] 周建钦[2] 

机构地区：[1]中国科学技术大学数学系,合肥230026 [2]安徽工业大学计算机系,马鞍山243002

出　　处：《应用数学学报》2007年第1期129-137,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金资助项目(60473142);安徽省教育厅自然科学研究(2006KJ238B)资助项目

摘　　要：双环网络是计算机互连网络和通讯系统的一类重要拓扑结构．1993年,李乔等人提出一个系统的构造方法,构造出69类0紧优和33类1紧优双环网络的无限族,并提出研究下述问题:求k(k>1)紧优双环网络的无限族．2003年,徐俊明等人给出一个4紧优双环网络的无限族．本文首先证明从每一个具体的0紧优双环网络出发,都可以构造若干0紧优双环网络无限族;结合同余方程组理论和数论中的素数理论,给出若干求一般k(k≥0)紧优双环网络无限族(包括非单位步长双环网络无限族)的方法．Double-loop networks have been widely studied as architecture for local area networks. In 1993, Li and Xu et al. presented a systematic method to construct optimal DLN and listed 69 infinite families of 0-tight optimal DLN and 33 infinite families of 1-tight optimal DLN, and proposed a problem of finding infinite families of k-tight （k ≥ 0） optimal double loop networks. In 2003, Xu et al. found one infinite family of 4-tight optimal DLN. In this paper, it is proved that some infinite families of 0-tight double loop networks can be constructed from every 0-tight double loop network. Combining with Chinese remainder theorem and prime number theory, we also present several approaches to construct some infinite families of k-tight （k ≥ 0） optimal double loop networks （including double loop networks with non-unit steps）.

关 键 词：双环网络 直径 紧优 无限族 素数 

分 类 号：O157.9[理学—数学] TP302[理学—基础数学]