【摘要】：信息時(shí)代的網(wǎng)絡(luò)給人們帶來前所未有的便捷,同時(shí)人類對(duì)網(wǎng)絡(luò)的依賴也日益增強(qiáng).近幾十年來,由于網(wǎng)絡(luò)中斷而造成重大損失的事故接連發(fā)生,其中一個(gè)重要原因是抗毀性不強(qiáng).因而,網(wǎng)絡(luò)抗毀性分析和設(shè)計(jì)問題受到了廣泛的關(guān)注.通常用連通圖作為網(wǎng)絡(luò)的模型,其抗毀性指的是抵抗外在破壞的能力.網(wǎng)絡(luò)抗毀性研究的方法是通過適當(dāng)?shù)膮?shù)定量刻畫為了中斷部分節(jié)點(diǎn)之間的聯(lián)絡(luò)需要付出的“最小”代價(jià)和網(wǎng)絡(luò)剩余部分的狀態(tài),分為(傳統(tǒng)的)抗毀性和鄰域抗毀性兩部分.抗毀性研究開展較早,成果比較豐富;鄰域抗毀性研究起步較晚,是針對(duì)網(wǎng)絡(luò)遭到破壞后造成的連鎖反應(yīng).鄰域抗毀性參數(shù)主要有鄰域連通度、鄰域完整度、鄰域離散數(shù)等.堅(jiān)韌度被認(rèn)為是最好的抗毀性參數(shù).本文將此概念和鄰域相結(jié)合,引入一個(gè)新參數(shù)---鄰域堅(jiān)韌度,作為已有鄰域抗毀性參數(shù)的補(bǔ)充.在給出幾類基本圖的鄰域堅(jiān)韌度計(jì)算公式基礎(chǔ)上,重點(diǎn)研究了聯(lián)圖、路和圈的笛卡爾積圖的鄰域堅(jiān)韌度及相互關(guān)系.本文的研究表明,用鄰域堅(jiān)韌度量化網(wǎng)絡(luò)的鄰域抗毀性,通常比其它參數(shù)效果更好.全文共分五部分,具體內(nèi)容安排如下.第一部分介紹了網(wǎng)絡(luò)抗毀性的相關(guān)概念及其研究現(xiàn)狀.第二部分是抗毀性參數(shù)與鄰域抗毀性參數(shù)主要研究?jī)?nèi)容和成果總結(jié).第三部分提出鄰域堅(jiān)韌度的概念,給出路、圈、星等基本圖類和廣義Petersen圖、復(fù)合圖的鄰域堅(jiān)韌度計(jì)算公式.第四部分是本文重點(diǎn)研究?jī)?nèi)容,完全解決了路和圈的笛卡爾積圖的鄰域堅(jiān)韌度計(jì)算問題,通過比較參數(shù)值揭示了這三類圖在鄰域抗毀性上的差異.第五部分總結(jié)全文,提出若干值得繼續(xù)研究的問題.
[Abstract]:The network of the information age brings people unprecedented convenience, at the same time, the dependence of the human to the network is also increasing day by day. In recent decades, serious losses caused by network disruption occurred one after another, one of the important reasons is that the invulnerability is not strong. Therefore, network invulnerability analysis and design issues have received extensive attention. Usually, connectivity graph is used as the model of network, and its invulnerability refers to the ability to resist external damage. The research method of network invulnerability is to quantitatively describe the "minimum" cost and the state of the rest of the network in order to interrupt the connections between nodes by appropriate parameters, which can be divided into two parts: (traditional) invulnerability and neighborhood invulnerability. The research on invulnerability was carried out earlier and the results were rich, and the research on neighborhood invulnerability started late, which was aimed at the chain reaction caused by the destruction of the network. Neighborhood invulnerability parameters include neighborhood connectivity, neighborhood integrity, neighborhood dispersion and so on. Toughness is considered to be the best invulnerability parameter. In this paper, this concept is combined with neighborhood and a new parameter, neighborhood toughness, is introduced as a supplement to existing neighborhood invulnerability parameters. Based on the calculation formulas of neighborhood toughness of some basic graphs, the neighborhood toughness and their relations of Cartesian product graphs of graphs, paths and cycles are studied in detail. The research in this paper shows that the neighborhood invulnerability of the network is usually better than that of other parameters by using the neighborhood toughness to quantify the neighborhood invulnerability of the network. The full text is divided into five parts, the specific contents are arranged as follows. The first part introduces the concept of network invulnerability and its research status. The second part is the main research content and achievement summary of invulnerability parameter and neighborhood invulnerability parameter. In the third part, the concept of neighborhood toughness is proposed, and the formulas for calculating neighborhood toughness of cycle, magnitude class, generalized Petersen graph and composite graph are given. The fourth part is the focus of this paper, which completely solves the calculation problem of neighborhood toughness of Cartesian product graphs of path and cycle, and reveals the difference in neighborhood invulnerability of these three kinds of graphs by comparing the parameter values. The fifth part summarizes the full text and puts forward some problems worthy of further study.
【學(xué)位授予單位】：西安建筑科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 劉二強(qiáng);;堅(jiān)韌度下的彩虹連通數(shù)[J];通化師范學(xué)院學(xué)報(bào);2015年02期

2 江秉華;陳金陽;王志平;;圖的平均邊連通度[J];北華大學(xué)學(xué)報(bào)(自然科學(xué)版);2013年06期

3 張勝貴,李學(xué)良,王力工;通信系統(tǒng)抗破壞能力研究[J];西北工業(yè)大學(xué)學(xué)報(bào);2002年01期

4 許進(jìn);論圖的堅(jiān)韌度(Ⅱ)[J];電子科學(xué)學(xué)刊;1996年S1期

相關(guān)碩士學(xué)位論文 前1條

1 魏宗田;關(guān)于網(wǎng)絡(luò)穩(wěn)定性參數(shù)的研究[D];西北工業(yè)大學(xué);2003年

，

本文編號(hào)：2453205