【摘要】：互連網(wǎng)絡(luò)是超級計算機的重要組成部分.在設(shè)計和選擇一個互連網(wǎng)絡(luò)的拓撲結(jié)構(gòu)時,哈密爾頓性和可靠性是評估網(wǎng)絡(luò)性能的重要指標,而條件連通度和限制連通度為衡量網(wǎng)絡(luò)的可靠性提供了度量參數(shù). 本文討論了完全對換網(wǎng)絡(luò)和三角塔網(wǎng)絡(luò)拓撲結(jié)構(gòu)中的幾個問題,主要工作如下： 1.對完全對換網(wǎng)絡(luò)提出如下一簇猜想：對任意整數(shù)n≥3,當n=0(mod4)或1(mod4)時,完全對換網(wǎng)絡(luò)CTn是k(1≤k≤n(n-1)/4)個邊不交的哈密爾頓圈和(n(n-1)／2-2k)個完美對集的并；當n=2(mod4)或3(mod4)時,完全對換網(wǎng)絡(luò)CTn是k(1≤k≤(n(n-1)-2)／4)個邊不交的哈密爾頓圈和(n(n-1)／2-2k)個完美對集的并；并證明了當n=4,n=5(1≤k≤4)和n=6(1≤k≤6)時,這簇猜想成立. 2.給出完全對換網(wǎng)絡(luò)的條件點連通度和限制點(邊)連通度.其中完全對換網(wǎng)絡(luò)CTn條件點連通度結(jié)果如下：當n≥4時,k1(CTn)=n(n-1)-2；當n≥5時,k2(CTn)=2n(n-1)-10.CTn的限制點(邊)連通度結(jié)果如下：當n≥4時,當n≥3時, 3.給出三角塔網(wǎng)絡(luò)的條件點連通度和限制點(邊)連通度.其中三角塔網(wǎng)絡(luò)TTn的條件點連通度結(jié)果如下：當n≥4時,k1(TTn)=4n-8；當n=4時,k2(TTn)=8；當n≥5時,k2(TTn)=8n-22.TTn的限制點(邊)連通度結(jié)果如下：當n≥4時,k2(TTn)=4n-8；當n=4時,k3(TT4)=8；當n≥5時,K3(TTn)=6n-15；當n≥3時,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，

本文編號：2247320