Proof of conjectures involving the largest and the smallest signless Laplacian eigenvalues of graphs

被引：20

作者：

Das, Kinkar Ch ^{[1
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

来源：

DISCRETE MATHEMATICS | 2012年 / 312卷 / 05期

关键词：

Graph; Signless Laplacian matrix; The largest signless Laplacian eigenvalue; The smallest signless Laplacian eigenvalue; SPECTRUM;

D O I：

10.1016/j.disc.2011.10.030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G = (V, E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G) = D(G) + A(G). In [5], Cvetkovic et al. (2007) have given conjectures on signless Laplacian eigenvalues of G (see also Aouchiche and Hansen (2010)[1], Oliveira et al. (2010) [14]). Here we prove two conjectures. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：992 / 998

页数：7

共 18 条

[11]

Ellingham M.N., 1993, Australas. J. Combin., V8, P247

[12] Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order [J].

Fan, Yi-Zheng ;

Tam, Bit-Shun ;

Zhou, Jun .

LINEAR & MULTILINEAR ALGEBRA, 2008, 56 (04) :381-397

[13]

Heuvel JV, 1995, LINEAR ALGEBRA APPL, V226-228, P723

[14] Bounds on the Q-spread of a graph [J].

Oliveira, Carla Silva ;

de Lima, Leonardo Silva ;

Maia de Abreu, Nair Maria ;

Kirkland, Steve .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (09) :2342-2351

[15] Q-integral graphs with edge-degrees at most five [J].

Simic, Slobodan K. ;

Stanic, Zoran .

DISCRETE MATHEMATICS, 2008, 308 (20) :4625-4634

[16]

Zhang F., 1999, Matrix Theory: Basic Results and Techniques

[17] The signless Laplacian spectral radius of graphs with given degree sequences [J].

Zhang, Xiao-Dong .

DISCRETE APPLIED MATHEMATICS, 2009, 157 (13) :2928-2937

[18] The lollipop graph is determined by its Q-spectrum [J].

Zhang, Yuanping ;

Liu, Xiaogang ;

Zhang, Bingyan ;

Yong, Xuerong .

DISCRETE MATHEMATICS, 2009, 309 (10) :3364-3369

← 1 2 →