关于图的关联控制的稳定性研究

发布时间：2018-06-22 15:40

本文选题：关联控制 + 关联加强　；参考：《山东科技大学》2017年硕士论文

【摘要】：图的理论知识论从诞生之日到目前为止已经历经了近三个世纪的岁月。图的着色理论经历了从点到边,再到特殊的这样一个进化的过程。那么,控制理论作为图论中及其重要的一环,也会经历这样的过程。于是图的控制理论开始从点萌发,经历了过对边的研究。随着对经典控制理论研究的加深,加上现实中的实际情况提出的具体要求,科学家们提出了各种各样的控制理论,经典控制理论是基础(这些理论要么是通过对经典控制的演化而来的,要么是对经典控制施加相应的限制因素)本文主要研究图的关联控制的稳定性并给出了部分图的关联控制数(控制参数就是所对应的最小控制集元素的数目。在对参数的探索过程中,一定会重点探究最小的控制集的相关性质,并且会探究它所对应的参数)。将关联控制的概念与加强数和约束数的概念进行融合,提出关联加强数和关联约束数的定义。关联控制的稳定性由关联加强数和关联约束数来体现。Fink在第一次提出使用约束数来计算互连网络的稳定性。在互联网络(图)中至少删除几条边,才会让互联网络(图)控制参数变大,此时去掉的边数就是约束数。由于控制数与关联控制数已确定为N-P问题,故而关联加强数和关联约束数也是N-P问题,本文给出几种特殊图的关联加强数和关联约束数的确切值。
[Abstract]:The theory of graph theory has gone through nearly three centuries since its birth. The coloring theory of graphs has undergone a process of evolution from point to edge and then to a special one. Then, as an important part of graph theory, control theory also goes through this process. So the control theory of graph began to germinate from the point and experienced the research of the opposite side. With the deepening of the study of classical control theory and the specific requirements of the actual situation in reality, scientists have put forward a variety of control theories. Classical control theories are fundamental (these theories are either derived from the evolution of classical control, In this paper, we mainly study the stability of the associated control of graphs and give the associated control number of some graphs (the control parameter is the number of the corresponding minimum control set elements). In the process of exploring the parameters, we will focus on the properties of the smallest control set and the corresponding parameters. The concept of association control is fused with the concepts of reinforcement number and constraint number, and the definition of association strengthening number and associated constraint number is proposed. The stability of the correlation control is represented by the correlation enhancement number and the correlation constraint number. In the first time, Fink proposed the use of the constraint number to calculate the stability of the interconnection network. Only when at least a few edges are deleted in the Internet (graph), the control parameters of the Internet (graph) become larger, and the number of edges removed is the number of constraints. Because the control number and the correlation control number have been determined to be N-P problem, so the correlation enhancement number and the correlation constraint number are also N-P problems. In this paper, the exact values of the association strengthening number and the correlation constraint number of several special graphs are given.
【学位授予单位】：山东科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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