| 若干图的谱性质研究 |
| Alternative Title | Spectral properties of a number of graphs
|
| 王井玉 |
| Thesis Advisor | 罗彦锋
|
| 2010-05-30
|
| Degree Grantor | 兰州大学
|
| Place of Conferral | 兰州
|
| Degree Name | 硕士
|
| Keyword | 完全图
邻接谱
共谱图
Laplacian谱
特征值
|
| Abstract | 本文主要刻画了完全二部图的邻接谱的特征并且证明了第四大Laplacian特征值小于2的树是由Laplacian谱确定的.
文章分为四章. 在第一章中, 介绍了谱确定问题的研究背景及现状;
在第二章中, 给出了与本文有关的基本概念及基本引理; 在第三章中,讨论了完全二部图邻接谱的特征; 在第四章中,给出了第四大Laplacian特征值小于2的树是由Laplacian谱确定的. |
| Other Abstract | In this thesis, we will characterize the adjacency spectrum of the complete bipartite graphs. Besides, we will show that
trees with fourth Laplacian eigenvalue less than two are determined by their Laplacian spectrum.
There are four chapters in this thesis. In chapter 1, the background and development of the spectral graph theory are introduced; In chapter 2, some concepts and known results which will be used in the last two chapters of this thesis are given; In chapter 3, the adjacency spectrum of complete bipartite graphs are characterized; In chapter 4, we show that trees with fourth Laplacian eigenvalue less than two are determined by their Laplacian spectrum. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/224761
|
| Collection | 数学与统计学院
|
Recommended Citation
GB/T 7714 |
王井玉. 若干图的谱性质研究[D]. 兰州. 兰州大学,2010.
|
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