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

被引：19

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

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