图的邻域坚韧度研究
发布时间：2019-04-03 12:18
【摘要】：信息时代的网络给人们带来前所未有的便捷,同时人类对网络的依赖也日益增强.近几十年来,由于网络中断而造成重大损失的事故接连发生,其中一个重要原因是抗毁性不强.因而,网络抗毁性分析和设计问题受到了广泛的关注.通常用连通图作为网络的模型,其抗毁性指的是抵抗外在破坏的能力.网络抗毁性研究的方法是通过适当的参数定量刻画为了中断部分节点之间的联络需要付出的“最小”代价和网络剩余部分的状态,分为(传统的)抗毁性和邻域抗毁性两部分.抗毁性研究开展较早,成果比较丰富;邻域抗毁性研究起步较晚,是针对网络遭到破坏后造成的连锁反应.邻域抗毁性参数主要有邻域连通度、邻域完整度、邻域离散数等.坚韧度被认为是最好的抗毁性参数.本文将此概念和邻域相结合,引入一个新参数---邻域坚韧度,作为已有邻域抗毁性参数的补充.在给出几类基本图的邻域坚韧度计算公式基础上,重点研究了联图、路和圈的笛卡尔积图的邻域坚韧度及相互关系.本文的研究表明,用邻域坚韧度量化网络的邻域抗毁性,通常比其它参数效果更好.全文共分五部分,具体内容安排如下.第一部分介绍了网络抗毁性的相关概念及其研究现状.第二部分是抗毁性参数与邻域抗毁性参数主要研究内容和成果总结.第三部分提出邻域坚韧度的概念,给出路、圈、星等基本图类和广义Petersen图、复合图的邻域坚韧度计算公式.第四部分是本文重点研究内容,完全解决了路和圈的笛卡尔积图的邻域坚韧度计算问题,通过比较参数值揭示了这三类图在邻域抗毁性上的差异.第五部分总结全文,提出若干值得继续研究的问题.
[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.
【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：2453205
[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.
【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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