A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph

被引：52

作者：

Shu, JL ^{[1
]}

Hong, Y ^{[1
]}

Wen-Ren, K ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2002年 / 347卷 / 1-3期

基金：

中国国家自然科学基金;

关键词：

line graph; degree sequence; adjacency spectral radius; Laplacian spectral radius;

D O I：

10.1016/S0024-3795(01)00548-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a simple connected graph with it vertices. The largest eigenvalue of the Laplacian matrix of G is denoted by V (G). Suppose the degree sequence of G is d(1) greater than or equal to d(2) greater than or equal to ...greater than or equal tod(n). In this paper, we present a sharp upper bound of mu (G) mu(G) less than or equal to d(n) + 1/2 + root(d(n) - 1/2)(2) + Sigma(i=1)(n) d(i)(d(i) - d(n)), the equality holds if and only if G is a regular bipartite graph. (C) 2002 Published by Elsevier Science Inc.

引用

页码：123 / 129

页数：7

共 50 条

[21] A decreasing sequence of upper bounds on the largest Laplacian eigenvalue of a graph
Rojo, O
Rojo, H
LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 381 : 97 - 116
[22] On thek-th largest eigenvalue of the Laplacian matrix of a graph
Zhang Xiaodong
Li Jiongsheng
Acta Mathematicae Applicatae Sinica, 2001, 17 (2) : 183 - 190
[23] AN UPPER BOUND FOR THE LARGEST EIGENVALUE OF A GRAPH - EFFECT OF TYPES OF VERTICES
TURKER, L
JOURNAL OF MATHEMATICAL CHEMISTRY, 1992, 9 (04) : 341 - 349
[24] On the third largest Laplacian eigenvalue of a graph
Guo, Ji-Ming
LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (01): : 93 - 102
[25] An eigenvalue bound for the Laplacian of a graph
Grossman, JP
DISCRETE MATHEMATICS, 2005, 300 (1-3) : 225 - 228
[26] A characterization on graphs which achieve the upper bound for the largest Laplacian eigenvalue of graphs
Das, KC
LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 376 : 173 - 186
[27] A new upper bound for eigenvalues of the Laplacian matrix of a graph
Li, JS
Zhang, XD
LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 265 : 93 - 100
[28] A new upper bound for eigenvalues of the Laplacian matrix of a graph
Li, Jiong-Sheng
Zhang, Xiao-Dong
Linear Algebra and Its Applications, 1997, 265 (1-3): : 93 - 100
[29] A Sharp Upper Bound on the Least Signless Laplacian Eigenvalue Using Domination Number
Chang-Xiang He
Min Zhou
Graphs and Combinatorics, 2014, 30 : 1183 - 1192
[30] A Sharp Upper Bound on the Least Signless Laplacian Eigenvalue Using Domination Number
He, Chang-Xiang
Zhou, Min
GRAPHS AND COMBINATORICS, 2014, 30 (05) : 1183 - 1192

← 1 2 3 4 5 →