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基于拉普拉斯谱确定的两类树

张涛1,2,*    白延琴1   

  1. 1. 上海大学理学院数学系, 上海 200444; 2. 武警政治学院, 上海 201602
  • 收稿日期:2016-07-08 出版日期:2017-03-15 发布日期:2017-03-15
  • 通讯作者: 张涛 snowyjune@163.com
  • 基金资助:

    国家自然科学基金(No. 11371242)

Two families of trees determined by  their Laplacian spectrum

ZHANG Tao1,2,*    BAI Yanqin1   

  1. 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, China; 2. PAP Institute of Politics, Shanghai 201602, China
  • Received:2016-07-08 Online:2017-03-15 Published:2017-03-15

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摘要：

设图G是简单连通图. 如果任何一个与图G关于拉普拉斯矩阵同谱的图, 都与图G同构, 称图G可由其拉普拉斯谱确定. 定义了树Y_n和树F(2,n,1)两类特殊结构的树. 利用同谱图线图的特点, 证明了树Y_n和树F(2,n,1)可由其拉普拉斯谱确定.

关键词: 图谱, 同谱图, 特征值, 拉普拉斯谱

Abstract:

Let G be a simple connected graph. A graph G is called to be determined by its Laplacian spectrum if any graph having the same Laplacian spectrum as G is isomorphic to G. In this paper, tree Y_n and tree F(2,n,1) which have special structures are defined. It is proved that these two families of trees are determined by their Laplacian spectrum, considering the properties of the line graphs of  the cospectral graphs.

Key words: spectrum of a graph, cospectral graphs, eigenvalue, Laplacian spectrum