兰州大学机构库 >数学与统计学院
若干图的谱性质研究
Alternative TitleSpectral 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 AbstractIn 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
Language中文
Document Type学位论文
Identifierhttps://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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