图的参数控制研究

发布时间：2018-11-14 12:09

【摘要】：图的控制参数理论是图论研究领域发展较快一个分支,图的控制理论的研究有着重大的理论意义,并且与其他学科领域如组合优化,理论计算机科学等都有着密切的联系。图的控制参数理论在现实生活中也有着广泛的应用,如设施选址、通信网络、监控系统和军事部署等方面。基于不同的实际背景,图论研究者在图的经典控制理论基础上定义了许多图的参数控制,如图的符号控制、图的k-距离控制、图的边控制、图的符号边控制、图的罗马控制、图的逆罗马控制、图的集控制等等。本文主要研究图的逆罗马控制、图的符号边k-距离控制和图的符号团边划分数。本文分为四章：第一章介绍了本文所涉及的有关基本概念和定义,对本文所研究问题的国内外研究现状作了详细介绍,并详细列出了本文的主要研究结果。第二章主要研究了一些特殊图类的逆罗马控制数,如路、圈等的逆罗马控制数,得到了其精确值,并证明了任意图G的逆罗马控制数的上下界。第三章讨论了图的符号边k-距离控制数,研究当κ=1时一些简单图的符号边k-距离控制数,得到了路、圈和轮等图的符号边k-距离控制数的精确值,并证明了任意图G的符号边k-距离控制数的上下界。第四章基于图的符号边划分数的定义和现实背景,把图的符号边划分数的概念推广到图的符号团边划分数上。本章节主要以图的极大团的团数为主线研究了一般n阶图G的符号团边划分数。证明了n阶图G的符号团边划分数与该图G的极大团的团数ω的关系,得出一般图的符号团边划分数。
[Abstract]:The control parameter theory of graph is a branch of graph theory. The study of control theory of graph has great theoretical significance and is closely related to other disciplines such as combinatorial optimization and theoretical computer science. The control parameter theory of graph has been widely used in real life, such as facility location, communication network, monitoring system and military deployment. On the basis of the classical control theory of graphs, graph theorists have defined a lot of graph parameter control, such as graph symbol control, graph k-distance control, graph edge control, graph symbol edge control, graph Roman control, graph control based on different practical background. Inverse Roman control of graphs, set control of graphs, and so on. In this paper, we mainly study the inverse Roman control of graphs, the symbolic edge k- distance control of graphs and the number of symbolic clique partitioning of graphs. This paper is divided into four chapters: the first chapter introduces the basic concepts and definitions involved in this paper, gives a detailed introduction of the domestic and foreign research status of the problems studied in this paper, and lists the main research results in detail. In the second chapter, we study the inverse Roman domination numbers of some special graphs, such as paths, cycles and so on, and obtain their exact values, and prove the upper and lower bounds of the inverse Roman domination numbers of any graph G. In chapter 3, the symbolic edge k- distance domination number of graphs is discussed. When 魏 = 1, the signed edge k- distance domination numbers of some simple graphs are studied, and the exact values of the signed edge k- distance domination numbers of graphs such as paths, cycles and wheels are obtained. The upper and lower bounds of the signed edge k distance domination number of any graph G are proved. In chapter 4, based on the definition of symbolic edge partition number of graphs and the realistic background, the concept of symbol edge partition number of graph is extended to the symbol edge partition number of graph. In this chapter, the number of symbolic clique partitioning of a graph G of order n is studied based on the number of maximal groups of graphs. In this paper, we prove the relation between the number of symbolic clique edge partitioning of graph G of order n and the number of maximal cliques 蠅 of the graph G, and obtain the number of symbolic clique edge partitioning of a general graph.
【学位授予单位】：浙江师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

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