Improved results on Brouwer's conjecture for sum of the Laplacian eigenvalues of a graph

被引：12

作者：

Chen, Xiaodan ^{[1
]}

机构：

[1] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Guangxi, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 557卷

基金：

中国国家自然科学基金;

关键词：

Brouwer's conjecture; Grone-Merris theorem; Sum of Laplacian eigenvalues; Clique number; Girth; Split graph; ENERGY;

D O I：

10.1016/j.laa.2018.08.003

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 M edges, and let S-k(G) be the sum of the k largest Laplacian eigenvalues of G. It was conjectured by Brouwer that S-k(G) <= m + (GRAPHICS) holds for 1 <= k <= n. In this paper, we present several families of graphs for which Brouwer's conjecture holds, which improve some previously known results. We also establish a new upper bound on S-k(G) for split graphs, which is tight for each k is an element of {1, 2, . . . , n - 1} and turns out to be better than that conjectured by Brouwer. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：327 / 338

页数：12

共 17 条

[11] On the sum of Laplacian eigenvalues of graphs [J].

Haemers, W. H. ;

Mohammadian, A. ;

Tayfeh-Rezaie, B. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (09) :2214-2221

[12] Spectral threshold dominance, Brouwer's conjecture and maximality of Laplacian energy [J].

Helmberg, Christoph ;

Trevisan, Vilmar .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 512 :18-31

[13]

Mayank, 2010, THESIS

[14] On the Laplacian eigenvalues of a graph and Laplacian energy [J].

Pirzada, S. ;

Ganie, Hilal A. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 486 :454-468

[15] Bounding the sum of the largest Laplacian eigenvalues of graphs [J].

Rocha, I. ;

Trevisan, V. .

DISCRETE APPLIED MATHEMATICS, 2014, 170 :95-103

[16] On a conjecture for the sum of Laplacian eigenvalues [J].

Wang, Shouzhong ;

Huang, Yufei ;

Liu, Bolian .

MATHEMATICAL AND COMPUTER MODELLING, 2012, 56 (3-4) :60-68

[17] On Laplacian eigenvalues of a graph [J].

Zhou, B .

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2004, 59 (03) :181-184

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