On matrices associated to directed graphs and applications

被引：2

作者：

de Freitas, Maria Aguieiras A. ^{[1
,2
]}

Bonifacio, Andrea Soares ^{[3
]}

Robbiano, Maria ^{[4
]}

San Martin, Bernardo ^{[4
]}

机构：

[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941 Rio De Janeiro, Brazil

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

[3] Univ Fed Estado Rio de Janeiro, Dept Informat Aplicada, Rio De Janeiro, Brazil

[4] Univ Catolica Norte, Dept Matemat, Coquimbo, Chile

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 442卷

关键词：

Graphs; Incidence matrix; (-1,0,1)-vertex-edge incidence matrix; Line graph; Laplacian matrix; Signless Laplacian matrix; Energy; LAPLACIAN SPECTRUM; ENERGY;

D O I：

10.1016/j.laa.2013.07.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the notions of 0-incidence and 1-incidence between edges on a directed graph associated to the line graph of a graph. The Laplacian energy and the signless Laplacian energy are obtained in a new way. From these results a relation between both energies is derived. Moreover, we obtain lower bounds for both the largest Laplacian eigenvalue and the largest signless Laplacian eigenvalue and prove that the latter is strictly greater than the first one. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：156 / 164

页数：9

共 18 条

[11] Laplacian energy of a graph [J].

Gutman, I ;

Zhou, B .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 414 (01) :29-37

[12]

Gutman I., 1978, Ber. Math. Statist. Sekt. Forschungsz Graz., V103, DOI [DOI 10.1016/J.LAA.2004.02.038, DOI 10.1088/1742-5468/2008/10/P10008]

[13]

Gutman I, 2009, MATCH-COMMUN MATH CO, V62, P573

[14] On incidence energy of a graph [J].

Gutman, Ivan ;

Kiani, Dariush ;

Mirzakhah, Maryam ;

Zhou, Bo .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (08) :1223-1233

[15]

MERRIS R, 1994, LINEAR ALGEBRA APPL, V198, P143

[16]

Minc, 1988, NONNEGATIVE MATRICES

[17] On the sum of k largest singular values of graphs and matrices [J].

Nikiforov, Vladimir .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (10) :2394-2401

[18] Applications of a theorem by Ky Fan in the theory of graph energy [J].

So, Wasin ;

Robbiano, Maria ;

Maia de Abreu, Nair Maria ;

Gutman, Ivan .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (09) :2163-2169

← 1 2 →