恰有三个主特征值的树

J4 ›› 2013, Vol. 48 ›› Issue (6): 23-28.

恰有三个主特征值的树

孙德荣,徐兰

昌吉学院数学系，新疆昌吉 831100

收稿日期:2012-02-09 出版日期:2013-06-20 发布日期:2013-06-09
作者简介:孙德荣(1965- ),女,副教授,硕士,研究方向为图论及其应用. Email:1471983955@qq.com
基金资助:
新疆维吾尔自治区科学研究重点项目(XJEDU2012I38);昌吉学院研究群体基金项目(2011YJQT01);昌吉学院硕士研究生启动基金项目(2012SSQD012)

Trees with exactly three main eigenvalues

SUN De-rong, XU Lan

Department of Mathematics, Changji College, Changji 831100, Xinjiang, China

Received:2012-02-09 Online:2013-06-20 Published:2013-06-09

摘要/Abstract

摘要：

设λ是图G的一个特征值,如果存在属于λ的一个特征向量X=(x1,x2,…,xn)T,使得∑nk=1xk≠0,则称λ是图G的主特征值。通过讨论图的主特征值数与公平划分之间的联系,给出某些具有三个主特征值的树类及其主特征值的计算方法。

关键词: 主特征值;公平划分;树;计算

Abstract:

An eigenvalue of graphs is called a main eigenvalue if it has an eigenvector the sum of whose entries is not zero. By studying the relationship between the main eigenvalue and the equitable partition of graphs, it gives some trees with exactly three main eigenvalues and computing method of main eigenvalues.

Key words: main eigenvalue; equitable partition; trees; computational

孙德荣,徐兰. 恰有三个主特征值的树[J]. J4, 2013, 48(6): 23-28.

SUN De-rong, XU Lan. Trees with exactly three main eigenvalues[J]. J4, 2013, 48(6): 23-28.

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