Upper bounds for the sum of Laplacian eigenvalues of graphs

被引：35

作者：

Du, Zhibin ^{[2
]}

Zhou, Bo ^{[1
]}

机构：

[1] S China Normal Univ, Dept Math, Guangzhou 510631, Guangdong, Peoples R China

[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Laplacian eigenvalues; Trees; Unicyclic graphs; Bicyclic graphs;

D O I：

10.1016/j.laa.2012.01.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph with n vertices and e(G) edges, and let mu(1) (G) >= mu(2)(G) >= ... >= mu(n)(G) = 0 be the Laplacian eigenvalues of G. Let S-k(G) = Sigma(k)(i=1) mu(i)(G), where 1 <= k <= n. Brouwer conjectured that S-k(G) <= e(G) + ((k+1)(2)) for 1 <= k <= n. It has been shown in Haemers et al. [7] that the conjecture is true for trees. We give upper bounds for Sic (C). and in particular, we show that the conjecture is true for unicyclic and bicyclic graphs. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：3672 / 3683

页数：12

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