Bounds for the signless Laplacian energy

被引：58

作者：

Abreu, Nair ^{[2
]}

Cardoso, Domingos M. ^{[3
]}

Gutman, Ivan ^{[4
]}

Martins, Enide A. ^{[3
]}

Robbiano, Maria ^{[1
]}

机构：

[1] Univ Catolica Norte, Coquimbo, Chile

[2] Univ Fed Rio de Janeiro, BR-21941 Rio De Janeiro, Brazil

[3] Univ Aveiro, Aveiro, Portugal

[4] Univ Kragujevac, Kragujevac, Serbia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 10期

关键词：

Graph spectrum; Laplacian graph spectrum; Signless Laplacian spectrum; Laplacian energy; Signless Laplacian energy; GRAPHS; SPECTRUM;

D O I：

10.1016/j.laa.2010.10.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. The Laplacian (respectively, the signless Laplacian) energy of G is the sum of the absolute values of the differences between the eigenvalues of the Laplacian (respectively, signless Laplacian) matrix and the arithmetic mean of the vertex degrees of the graph. In this paper, among some results which relate these energies, we point out some bounds to them using the energy of the line graph of G. Most of these bounds are valid for both energies, Laplacian and signless Laplacian. However, we present two new upper bounds on the signless Laplacian which are not upper bounds for the Laplacian energy. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2365 / 2374

页数：10

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