【摘要】：組合數(shù)學(xué)是一門(mén)研究離散對(duì)象的科學(xué)，應(yīng)用十分廣泛。圖論是組合數(shù)學(xué)中的一個(gè)重要分支，它是解決幾何、數(shù)論、運(yùn)籌學(xué)和優(yōu)化等領(lǐng)域中各種組合問(wèn)題非常有用的工具。 本文主要結(jié)合圖論和集合論的相關(guān)知識(shí)，通過(guò)對(duì)本原有向圖中每個(gè)頂點(diǎn)經(jīng)過(guò)k長(zhǎng)途徑所到達(dá)點(diǎn)的集合進(jìn)行分析，得出幾個(gè)特殊本原有向圖的scrambling指數(shù)，廣義scrambling指數(shù)及廣義competition指數(shù)。 第一章：主要介紹了組合數(shù)學(xué)和圖論的基本概念及研究背景，給出了本原有向圖的scrambling指數(shù)、廣義scrambling指數(shù)與廣義competition指數(shù)的概念，，簡(jiǎn)述了本領(lǐng)域國(guó)內(nèi)外的研究現(xiàn)狀及進(jìn)展，最后列舉出本文所得出的一些主要結(jié)論。 第二章：研究三個(gè)特殊本原有向圖的scrambling指數(shù)。 第三章：研究三個(gè)特殊本原有向圖的廣義scrambling指數(shù)。 第四章：研究一個(gè)本原有向圖的廣義scrambling指數(shù)和廣義competition指數(shù)。
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O157.5

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本文編號(hào)：2470501