【摘要】：互連網(wǎng)絡(luò)是超級(jí)計(jì)算機(jī)的重要組成部分.在設(shè)計(jì)和選擇一個(gè)互連網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)時(shí),哈密爾頓性和可靠性是評(píng)估網(wǎng)絡(luò)性能的重要指標(biāo),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(duì)換網(wǎng)絡(luò)和三角塔網(wǎng)絡(luò)拓?fù)浣Y(jié)構(gòu)中的幾個(gè)問題,主要工作如下： 1.對(duì)完全對(duì)換網(wǎng)絡(luò)提出如下一簇猜想：對(duì)任意整數(shù)n≥3,當(dāng)n=0(mod4)或1(mod4)時(shí),完全對(duì)換網(wǎng)絡(luò)CTn是k(1≤k≤n(n-1)/4)個(gè)邊不交的哈密爾頓圈和(n(n-1)／2-2k)個(gè)完美對(duì)集的并；當(dāng)n=2(mod4)或3(mod4)時(shí),完全對(duì)換網(wǎng)絡(luò)CTn是k(1≤k≤(n(n-1)-2)／4)個(gè)邊不交的哈密爾頓圈和(n(n-1)／2-2k)個(gè)完美對(duì)集的并；并證明了當(dāng)n=4,n=5(1≤k≤4)和n=6(1≤k≤6)時(shí),這簇猜想成立. 2.給出完全對(duì)換網(wǎng)絡(luò)的條件點(diǎn)連通度和限制點(diǎn)(邊)連通度.其中完全對(duì)換網(wǎng)絡(luò)CTn條件點(diǎn)連通度結(jié)果如下：當(dāng)n≥4時(shí),k1(CTn)=n(n-1)-2；當(dāng)n≥5時(shí),k2(CTn)=2n(n-1)-10.CTn的限制點(diǎn)(邊)連通度結(jié)果如下：當(dāng)n≥4時(shí),當(dāng)n≥3時(shí), 3.給出三角塔網(wǎng)絡(luò)的條件點(diǎn)連通度和限制點(diǎn)(邊)連通度.其中三角塔網(wǎng)絡(luò)TTn的條件點(diǎn)連通度結(jié)果如下：當(dāng)n≥4時(shí),k1(TTn)=4n-8；當(dāng)n=4時(shí),k2(TTn)=8；當(dāng)n≥5時(shí),k2(TTn)=8n-22.TTn的限制點(diǎn)(邊)連通度結(jié)果如下：當(dāng)n≥4時(shí),k2(TTn)=4n-8；當(dāng)n=4時(shí),k3(TT4)=8；當(dāng)n≥5時(shí),K3(TTn)=6n-15；當(dāng)n≥3時(shí),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(hào)：2247320