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

共 50 条

[21] Bounds and conjectures for the signless Laplacian index of graphs
Hansen, Pierre
Lucas, Claire
LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (12) : 3319 - 3336
[22] Upper bounds on the (signless) Laplacian eigenvalues of graphs
Das, Kinkar Ch.
Liu, Muhuo
Shan, Haiying
LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 459 : 334 - 341
[23] On Zagreb index, signless Laplacian eigenvalues and signless Laplacian energy of a graph
S. Pirzada
Saleem Khan
Computational and Applied Mathematics, 2023, 42
[24] Eigenvalue bounds for the signless p-Laplacian
Borba, Elizandro Max
Schwerdtfeger, Uwe
ELECTRONIC JOURNAL OF COMBINATORICS, 2018, 25 (02):
[25] On the signless Laplacian energy of a digraph
Ganie, Hilal A.
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023,
[26] Signless Laplacian energy, distance Laplacian energy and distance signless Laplacian spectrum of unitary addition Cayley graphs
Naveen, Palanivel
Chithra, A. V.
LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (22): : 7514 - 7535
[27] Maximality of the signless Laplacian energy
Pinheiro, Lucelia Kowalski
Trevisan, Vilmar
DISCRETE MATHEMATICS, 2018, 341 (01) : 33 - 41
[28] On the distance signless Laplacian spectral radius and the distance signless Laplacian energy of graphs
Alhevaz, Abdollah
Baghipur, Maryam
Paul, Somnath
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2018, 10 (03)
[29] On (distance) Laplacian energy and (distance) signless Laplacian energy of graphs
Das, Kinkar Ch.
Aouchiche, Mustapha
Hansen, Pierre
DISCRETE APPLIED MATHEMATICS, 2018, 243 : 172 - 185
[30] Sharp bounds on the signless Laplacian spectral radii of graphs
Yu, Guanglong
Wu, Yarong
Shu, Jinlong
LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (03) : 683 - 687

← 1 2 3 4 5 →