几类图的谱刻画问题 Alternative Title Spectral Characterization of Several Classes of Graphs 夏海涛 Thesis Advisor 罗彦锋 2010-05-30 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 邻接谱 Laplace谱 谱确定 共谱图 Abstract 作为代数图理论的一个重要部分,图的谱理论主要研究图的邻接谱与图的Laplace谱.我们称一个图是由其邻接谱(或Laplace谱)确 定的,如果没有非同构的图具有相同的邻接谱(或Laplace谱). 全文分为五章.第一章介绍了图的谱确定问题的研究背景和现状;在第二章中,我们给出了后文将要用到的 基本定义和结论;在第三章中,我们将证明两类特殊的图是由它们的 Laplace谱确定的;在第四章,我们对一类双圈图的Laplace谱确定问题进行 刻画;在第五章,我们对一类单圈图的邻接谱和Laplace谱确定问题进行讨论. Other Abstract As an important part of algebraic graph theory, spectral graph theory mainly concerns with the adjacency spectrum and Laplacian spectrum of a graph. A graph is said to be determined by its adjacency spectrum (resp., Laplacian spectrum) if there is no other nonisomorphic graph with the same adjacency spectrum (resp.,Laplacian spectrum). There are five chapters in this thesis. The background and development of the spectral determined problem will be introduced in chapter 1; in chapter 2, we will present some basic definitions and results which will be used in the following chapters; in chapter 3, we will show that two kinds of special graphs are determined by their Laplacian spectrum; in chapter 4, we will investigate the spectral determined problem of a class of bicyclic graphs; in chapter 5, we will discuss whether a special graph with one cycle is determined by its adjacency or Laplacian spectrum. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225034 Collection 数学与统计学院 Recommended CitationGB/T 7714 夏海涛. 几类图的谱刻画问题[D]. 兰州. 兰州大学,2010.
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