图的毁裂度与边毁裂度相关问题研究
发布时间：2018-08-11 20:51
【摘要】：在计算机和通讯网络设计中,为了避免或最大限度地减少因网络中断造成的损失,抗毁性是必须考虑的重要因素.因此,网络设计的基本思想之一是使其在受到外部攻击时,不容易被破坏;更进一步,一旦受到破坏,也比较容易修复或重建.网络可以用一个连通图来表示,其抗毁性即所对应的图的抗毁性,通过引入适当的参数定量刻画.连通度和边连通度是最早的抗毁性参数.然而这两个参数在刻画网络抗毁性方面有一定的局限性,后来引入的坚韧度和边坚韧度、完整度和边完整度、粘连度和边粘连度、离散数、毁裂度和边毁裂度等参数,反映了“最坏”情形下破坏网络的难度和网络被破坏的程度,因此得到了较为深入的研究.针对毁裂度和边毁裂度的某些不足,本文引入一个新参数—弱毁裂度.给出了几类基本图和运算图的参数值计算、界以及与其它参数的关系,并在此基础上讨论了弱毁裂度的Nordhaus-Gaddum型问题.通过构造实例和比较的方法,得出该参数与抗毁性的一般结论:对于某些图类的抗毁性,弱毁裂度比粘连度、毁裂度和弱完整度的区分度更好.全文共分五个部分,具体安排如下.第一部分主要介绍了网络及其抗毁性的相关概念,抗毁性参数的研究背景、意义和研究现状.第二部分是毁裂度和边毁裂度的主要研究成果简介.第三部分引入弱毁裂度,给出了几类特殊图类弱毁裂度的计算公式,一般图的参数界,并初步探讨了弱毁裂度与其它抗毁性参数的关系.第四部分研究并给出几类运算图的弱毁裂度的计算公式或界.第五部分在总结全文的基础上,提出抗毁性参数进一步研究的若干问题.
[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.
【学位授予单位】：西安建筑科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
本文编号：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.
【学位授予单位】：西安建筑科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
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