【摘要】：信息時代的網(wǎng)絡給人們帶來前所未有的便捷,同時人類對網(wǎng)絡的依賴也日益增強.近幾十年來,由于網(wǎng)絡中斷而造成重大損失的事故接連發(fā)生,其中一個重要原因是抗毀性不強.因而,網(wǎng)絡抗毀性分析和設計問題受到了廣泛的關注.通常用連通圖作為網(wǎng)絡的模型,其抗毀性指的是抵抗外在破壞的能力.網(wǎng)絡抗毀性研究的方法是通過適當?shù)膮?shù)定量刻畫為了中斷部分節(jié)點之間的聯(lián)絡需要付出的“最小”代價和網(wǎng)絡剩余部分的狀態(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,是針對網(wǎng)絡遭到破壞后造成的連鎖反應.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.堅韌度被認為是最好的抗毀性參數(shù).本文將此概念和鄰域相結合,引入一個新參數(shù)---鄰域堅韌度,作為已有鄰域抗毀性參數(shù)的補充.在給出幾類基本圖的鄰域堅韌度計算公式基礎上,重點研究了聯(lián)圖、路和圈的笛卡爾積圖的鄰域堅韌度及相互關系.本文的研究表明,用鄰域堅韌度量化網(wǎng)絡的鄰域抗毀性,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)絡抗毀性的相關概念及其研究現(xiàn)狀.第二部分是抗毀性參數(shù)與鄰域抗毀性參數(shù)主要研究內(nèi)容和成果總結.第三部分提出鄰域堅韌度的概念,給出路、圈、星等基本圖類和廣義Petersen圖、復合圖的鄰域堅韌度計算公式.第四部分是本文重點研究內(nèi)容,完全解決了路和圈的笛卡爾積圖的鄰域堅韌度計算問題,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.
【學位授予單位】：西安建筑科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O157.5

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本文編號：2453205