k紧优双环网的无限族的构造

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)=3t2 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.

The Construction of Infinite Families of k-Tight Optimal Double Loop Networks

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}, A =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.