An always nontrivial upper bound for Laplacian graph eigenvalues

被引：44

作者：

Rojo, O

Soto, R

Rojo, H

机构：

[1] Univ Catolica Norte, Dept Matemat, Antofagasta, Chile

[2] Univ Antofagasta, Dept Matemat, Antofagasta, Chile

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 312卷 / 1-3期

关键词：

graph; Laplacian matrix; spectral radius;

D O I：

10.1016/S0024-3795(00)00104-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph on vertex set V = {v(1), v(2),..., v(n)}. Let d(i) be the degree of v(i), let N-i be the set of neighbours of v(i) and let /S/ be the number of vertices of S subset of or equal to V: In this note, we prove that max {d(i) + d(i) - /N-i boolean AND N-j/ : 1 less than or equal to i < j less than or equal to n} is an upper bound for the largest eigenvalue of the Laplacian matrix of G. For any G, this bound does not exceed the order of G. (C) 2000 Elsevier Science Inc. All rights reserved. AMS classification: 05C50.

引用

页码：155 / 159

页数：5

共 5 条

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[2]

Bauer F.L., 1969, LINEAR ALGEBRA APPL, V2, P275

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