On the sum of Laplacian eigenvalues of graphs

被引：45

作者：

Haemers, W. H. ^{[1
]}

Mohammadian, A. ^{[2
,3
]}

Tayfeh-Rezaie, B. ^{[3
]}

机构：

[1] Tilburg Univ, Dept Econometr & Operat Res, NL-5000 LE Tilburg, Netherlands

[2] Amirkabir Univ Technol, Fac Math & Comp Sci, Tehran, Iran

[3] IPM, Sch Math, Inst Res Fundamental Sci, Tehran, Iran

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 09期

关键词：

Laplacian eigenvalues of a graph; Sum of eigenvalues; Largest eigenvalue;

D O I：

10.1016/j.laa.2009.03.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured that the sum of the k largest Laplacian eigen-values of G is at most e(G) + ((2) (k + 1)), where e(G) is the number of edges of G. We prove this conjecture for k = 2. We also show that if G is a tree, then the sum of the k largest Laplacian eigenvalues of G is at most e(G) + 2k - 1. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2214 / 2221

页数：8

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