四个本原有向图的scrambling指数和广义competition指数

发布时间：2019-05-06 21:16

【摘要】：组合数学是一门研究离散对象的科学，应用十分广泛。图论是组合数学中的一个重要分支，它是解决几何、数论、运筹学和优化等领域中各种组合问题非常有用的工具。本文主要结合图论和集合论的相关知识，通过对本原有向图中每个顶点经过k长途径所到达点的集合进行分析，得出几个特殊本原有向图的scrambling指数，广义scrambling指数及广义competition指数。第一章：主要介绍了组合数学和图论的基本概念及研究背景，给出了本原有向图的scrambling指数、广义scrambling指数与广义competition指数的概念，，简述了本领域国内外的研究现状及进展，最后列举出本文所得出的一些主要结论。第二章：研究三个特殊本原有向图的scrambling指数。第三章：研究三个特殊本原有向图的广义scrambling指数。第四章：研究一个本原有向图的广义scrambling指数和广义competition指数。
[Abstract]:Combinatorial mathematics is a science that studies discrete objects and is widely used. Graph theory is an important branch of combinatorial mathematics. It is a very useful tool for solving various combinatorial problems in the fields of geometry, number theory, operational research and optimization. In this paper, based on the knowledge of graph theory and set theory, the scrambling exponent, generalized scrambling index and generalized competition index of some special primitive digraphs are obtained by analyzing the set of points that each vertex reaches through the k-long path in the original digraph. In the first chapter, the basic concepts and research background of combinatorial mathematics and graph theory are introduced. The concepts of scrambling index, generalized scrambling index and generalized competition index of the original digraph are given, and the present situation and progress of the research in this field at home and abroad are summarized. Finally, some main conclusions obtained in this paper are listed. In chapter 2, we study the scrambling exponents of three special original digraphs. In chapter 3, we study the generalized scrambling exponents of three special primitive digraphs. In chapter 4, we study the generalized scrambling exponent and generalized competition exponent of a primitive digraph.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

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