圖的毀裂度與邊毀裂度相關(guān)問題研究
發(fā)布時間：2018-08-11 20:51
【摘要】：在計算機和通訊網(wǎng)絡(luò)設(shè)計中,為了避免或最大限度地減少因網(wǎng)絡(luò)中斷造成的損失,抗毀性是必須考慮的重要因素.因此,網(wǎng)絡(luò)設(shè)計的基本思想之一是使其在受到外部攻擊時,不容易被破壞;更進一步,一旦受到破壞,也比較容易修復(fù)或重建.網(wǎng)絡(luò)可以用一個連通圖來表示,其抗毀性即所對應(yīng)的圖的抗毀性,通過引入適當?shù)膮?shù)定量刻畫.連通度和邊連通度是最早的抗毀性參數(shù).然而這兩個參數(shù)在刻畫網(wǎng)絡(luò)抗毀性方面有一定的局限性,后來引入的堅韌度和邊堅韌度、完整度和邊完整度、粘連度和邊粘連度、離散數(shù)、毀裂度和邊毀裂度等參數(shù),反映了“最壞”情形下破壞網(wǎng)絡(luò)的難度和網(wǎng)絡(luò)被破壞的程度,因此得到了較為深入的研究.針對毀裂度和邊毀裂度的某些不足,本文引入一個新參數(shù)—弱毀裂度.給出了幾類基本圖和運算圖的參數(shù)值計算、界以及與其它參數(shù)的關(guān)系,并在此基礎(chǔ)上討論了弱毀裂度的Nordhaus-Gaddum型問題.通過構(gòu)造實例和比較的方法,得出該參數(shù)與抗毀性的一般結(jié)論:對于某些圖類的抗毀性,弱毀裂度比粘連度、毀裂度和弱完整度的區(qū)分度更好.全文共分五個部分,具體安排如下.第一部分主要介紹了網(wǎng)絡(luò)及其抗毀性的相關(guān)概念,抗毀性參數(shù)的研究背景、意義和研究現(xiàn)狀.第二部分是毀裂度和邊毀裂度的主要研究成果簡介.第三部分引入弱毀裂度,給出了幾類特殊圖類弱毀裂度的計算公式,一般圖的參數(shù)界,并初步探討了弱毀裂度與其它抗毀性參數(shù)的關(guān)系.第四部分研究并給出幾類運算圖的弱毀裂度的計算公式或界.第五部分在總結(jié)全文的基礎(chǔ)上,提出抗毀性參數(shù)進一步研究的若干問題.
[Abstract]:In computer and communication network design, in order to avoid or minimize the loss caused by network interruption, invulnerability is an important factor to be considered. Therefore, one of the basic ideas of network design is that it is not easy to be destroyed when it is attacked from outside, and furthermore, it is easy to repair or rebuild once it is damaged. The network can be represented by a connected graph, whose invulnerability is the invulnerability of the corresponding graph, which is quantitatively characterized by introducing appropriate parameters. Connectivity and edge connectivity are the earliest invulnerability parameters. However, these two parameters have some limitations in describing the network's invulnerability. Some parameters, such as toughness and edge toughness, integrity and edge integrity, adhesion and edge adhesion, discrete number, destroyed crack and edge crack, are introduced later. It reflects the difficulty of destroying the network and the degree of the destruction of the network in the worst case, so it has been studied deeply. In this paper, a new parameter, weak fracture degree, is introduced to solve the defects of damage degree and edge damage degree. In this paper, we give the calculation of parameter values, bounds and relations with other parameters of some basic graphs and operation graphs, and discuss the Nordhaus-Gaddum type problem of weak fracture degree on this basis. Through the method of constructing examples and comparing, the general conclusion of the parameter and invulnerability is obtained: for some graphs, the degree of weak rupture is better than the degree of adhesion, the degree of destruction and the degree of weak integrity is better than that of the degree of adhesion, the degree of destruction and the degree of weak integrity. The full text is divided into five parts, the specific arrangements are as follows. The first part mainly introduces the network and its invulnerability related concepts, the research background, significance and research status of the invulnerability parameter. The second part is a brief introduction of the main research results of the breakage and edge damage. In the third part, the weak damage crack is introduced, the formulas for calculating the weak fracture of some special graphs and the parameter bounds of the general graph are given, and the relationship between the weak damage crack and other invulnerability parameters is discussed preliminarily. In the fourth part, the formulas or bounds for calculating the weak crack of some kinds of operation graphs are studied and given. In the fifth part, on the basis of summing up the whole paper, some problems of further research on invulnerability parameters are put forward.
【學(xué)位授予單位】：西安建筑科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5
本文編號：2178203
[Abstract]:In computer and communication network design, in order to avoid or minimize the loss caused by network interruption, invulnerability is an important factor to be considered. Therefore, one of the basic ideas of network design is that it is not easy to be destroyed when it is attacked from outside, and furthermore, it is easy to repair or rebuild once it is damaged. The network can be represented by a connected graph, whose invulnerability is the invulnerability of the corresponding graph, which is quantitatively characterized by introducing appropriate parameters. Connectivity and edge connectivity are the earliest invulnerability parameters. However, these two parameters have some limitations in describing the network's invulnerability. Some parameters, such as toughness and edge toughness, integrity and edge integrity, adhesion and edge adhesion, discrete number, destroyed crack and edge crack, are introduced later. It reflects the difficulty of destroying the network and the degree of the destruction of the network in the worst case, so it has been studied deeply. In this paper, a new parameter, weak fracture degree, is introduced to solve the defects of damage degree and edge damage degree. In this paper, we give the calculation of parameter values, bounds and relations with other parameters of some basic graphs and operation graphs, and discuss the Nordhaus-Gaddum type problem of weak fracture degree on this basis. Through the method of constructing examples and comparing, the general conclusion of the parameter and invulnerability is obtained: for some graphs, the degree of weak rupture is better than the degree of adhesion, the degree of destruction and the degree of weak integrity is better than that of the degree of adhesion, the degree of destruction and the degree of weak integrity. The full text is divided into five parts, the specific arrangements are as follows. The first part mainly introduces the network and its invulnerability related concepts, the research background, significance and research status of the invulnerability parameter. The second part is a brief introduction of the main research results of the breakage and edge damage. In the third part, the weak damage crack is introduced, the formulas for calculating the weak fracture of some special graphs and the parameter bounds of the general graph are given, and the relationship between the weak damage crack and other invulnerability parameters is discussed preliminarily. In the fourth part, the formulas or bounds for calculating the weak crack of some kinds of operation graphs are studied and given. In the fifth part, on the basis of summing up the whole paper, some problems of further research on invulnerability parameters are put forward.
【學(xué)位授予單位】：西安建筑科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5
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，本文編號：2178203
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