k紧优双环网的无限族的构造  

THE CONSTRUCTION OF INFINITE FAMILIES OF k-TIGHT OPTIMAL DOUBLE LOOP NETWORKS

作　　者：杨仕椿[1] 

机构地区：[1]阿坝师范高等专科学校数学系,汶川623000

出　　处：《系统科学与数学》2008年第7期780-790,共11页Journal of Systems Science and Mathematical Sciences

基　　金：四川省教育厅自然科学基金(2006C057)资助项目

摘　　要：双环网是计算机互连网络和通讯系统的一类重要拓扑结构,已广泛应用于计算机互连网络拓扑结构的设计中,利用L形瓦理论,结合中国剩余定理和二次同余方程的性质,给出了不同于参考文献中的任意k紧优双环网的无限族的构造方法,证明了对任意正整数k,若n(t)=3t^2+At+B,A=1,3,5,对于一定的B>(k+1)~2,均存在正整数t,使得{G(n(t);s(t))}是k紧优双环网的无限族,而且这样的无限族有无穷多类.作为定理的应用,给出了多类新的k紧优双环网的无限族.Double loop network is an important topological structure in computer networks and communication. Based on the theory of L-shaped tile, utilizing Chinese remainder theorem and some property of quadratic congruence, a method to construction of k-tight optimal infinite families of double loop networks is given, and the method is different from that in references. It is proved that there exist some k-tight optimal infinite families of double loop networks for every k 〉 0, where n（t） = 3t^2 ＋ At ＋ B for some B 〉 （k ＋ 1）^2, .4 = 1, 3, 5, and the infinite families are infinitesimal for every B. By using this method, we obtain some new k-tight optimal infinite families of double loop networks.

关 键 词：双环网 有向图 k紧优 无限族 直径 

分 类 号：O157.5[理学—数学]