完全对换网络和三角塔网络的若干性质

发布时间：2018-09-18 08:20

【摘要】：互连网络是超级计算机的重要组成部分.在设计和选择一个互连网络的拓扑结构时,哈密尔顿性和可靠性是评估网络性能的重要指标,而条件连通度和限制连通度为衡量网络的可靠性提供了度量参数. 本文讨论了完全对换网络和三角塔网络拓扑结构中的几个问题,主要工作如下： 1.对完全对换网络提出如下一簇猜想：对任意整数n≥3,当n=0(mod4)或1(mod4)时,完全对换网络CTn是k(1≤k≤n(n-1)/4)个边不交的哈密尔顿圈和(n(n-1)／2-2k)个完美对集的并；当n=2(mod4)或3(mod4)时,完全对换网络CTn是k(1≤k≤(n(n-1)-2)／4)个边不交的哈密尔顿圈和(n(n-1)／2-2k)个完美对集的并；并证明了当n=4,n=5(1≤k≤4)和n=6(1≤k≤6)时,这簇猜想成立. 2.给出完全对换网络的条件点连通度和限制点(边)连通度.其中完全对换网络CTn条件点连通度结果如下：当n≥4时,k1(CTn)=n(n-1)-2；当n≥5时,k2(CTn)=2n(n-1)-10.CTn的限制点(边)连通度结果如下：当n≥4时,当n≥3时, 3.给出三角塔网络的条件点连通度和限制点(边)连通度.其中三角塔网络TTn的条件点连通度结果如下：当n≥4时,k1(TTn)=4n-8；当n=4时,k2(TTn)=8；当n≥5时,k2(TTn)=8n-22.TTn的限制点(边)连通度结果如下：当n≥4时,k2(TTn)=4n-8；当n=4时,k3(TT4)=8；当n≥5时,K3(TTn)=6n-15；当n≥3时,A2(TTn)=4n-8,A3(TTn)=6n-13.
[Abstract]:Interconnection network is an important part of supercomputer. When designing and selecting the topology of an interconnect network, Hamiltonicity and reliability are important indexes to evaluate the network performance. The conditional connectivity and restricted connectivity provide the measurement parameters for the reliability of the network. In this paper, we discuss several problems in the topological structure of complete exchange network and triangular tower network. The main work is as follows: 1. The following conjecture is put forward for the complete commutation network: for any integer n 鈮，

本文编号：2247320