本文選題：循環(huán)圖 + 混合Cayley圖��； 參考：《新疆大學》2017年博士論文

【摘要】：隨著信息網(wǎng)絡(luò)的迅速發(fā)展,網(wǎng)絡(luò)的性能引起了人們的關(guān)注.信息網(wǎng)絡(luò)的拓撲結(jié)構(gòu)對網(wǎng)絡(luò)的性能起著決定性的作用.在設(shè)計多處理器網(wǎng)絡(luò)拓撲結(jié)構(gòu)時,網(wǎng)絡(luò)可靠性引起了人們的重視,網(wǎng)絡(luò)可靠性即網(wǎng)絡(luò)在它的某些部件(節(jié)點或者連接)發(fā)生故障時仍然能正常工作的能力.多處理器的互聯(lián)網(wǎng)絡(luò)通常被模型化為圖,因此,圖論中的一些經(jīng)典概念(比如連通度和邊連通度)就被用來研究網(wǎng)絡(luò)的可靠性.為了進一步研究,人們提出了大量在網(wǎng)絡(luò)優(yōu)化設(shè)計中具有深刻背景的連通性概念,如超(邊)連通性、圈點(邊)連通性、限制性(邊)連通性等等.本文主要研究混合Cayley圖的圈邊連通性,極小循環(huán)圖的圈點連通性,笛卡爾乘積圖的圈點連通性和限制性連通性,及半點傳遞有向圖的連通度問題.第一章,我們介紹了研究背景和一些基本概念,術(shù)語以及符號,并對各類圈邊連通性、圈點連通性、限制性連通性問題的研究現(xiàn)狀進行了一定程度的回顧.第二章,我們研究了混合Cayley圖的圈邊連通性問題,并描述了圈邊最優(yōu)的充要條件.第三章,我們刻畫了笛卡爾乘積圖的圈點連通度和限制性連通度.對于笛卡爾乘積圖,我們得到了圈點連通度的一個上界和下界,并對其3限制連通度和4限制連通度進行了研究,而對于κ≥ 5的限制性連通度,我們給出了兩個猜想.第四章,我們研究了極小循環(huán)圖的圈點連通度問題,并且給出對于任意的極小循環(huán)圖X = C(Z_n,S)≥ 12),其圈點連通度k_c(X)=g(k-2),其中g(shù)是圍長,κ(2)是正則度.第五章,我們對有向圖的連通度進行了研究,并給出半點傳遞圖的連通度等于該有向圖的最小度。
[Abstract]:With the rapid development of information network, the performance of network has attracted people's attention. The topology of the information network plays a decisive role in the performance of the network. In the design of multi-processor network topology, network reliability has attracted much attention. Network reliability is the ability of network to work normally when some of its components (nodes or connections) fail. Multiprocessor networks are usually modeled as graphs, so some classical concepts in graph theory, such as connectivity and edge connectivity, are used to study the reliability of networks. For further study, a large number of connectedness concepts with profound background in network optimization design have been proposed, such as hyperconnectivity, cycle point connectivity, restricted connectivity and so on. In this paper, we study the cycle edge connectivity of mixed Cayley graphs, the cycle vertex connectivity of minimal cyclic graphs, the cycle point connectivity and restricted connectivity of Cartesian product graphs, and the connectivity of semipoint transitive digraphs. In the first chapter, we introduce the research background, some basic concepts, terms and symbols, and review the current research status of the problems of cycle edge connectivity, cycle point connectivity and restricted connectivity to a certain extent. In chapter 2, we study the cycle edge connectivity of mixed Cayley graphs and describe the necessary and sufficient conditions for cycle edge optimization. In chapter 3, we characterize the cycle point connectivity and restricted connectivity of Cartesian product graphs. For Cartesian product graphs, we obtain an upper bound and a lower bound of the connectivity of cycle points, and study its 3-restricted connectivity and 4-restricted connectivity. For the restricted connectivity of 魏 鈮，

本文編號：1824073