Bounds on the (Laplacian) spectral radius of graphs

被引：41

作者：

Shi, Lingsheng ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2007年 / 422卷 / 2-3期

关键词：

spectral radius; Laplacian spectral radius; Nordhaus-Gaddum type; LARGEST EIGENVALUE; SHARP UPPER;

D O I：

10.1016/j.laa.2006.12.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The spectral radius of a graph is the largest eigenvalue of adjacency matrix of the graph and its Laplacian spectral radius is the largest eigenvalue of the Laplacian matrix which is the difference of the diagonal matrix of vertex degrees and the adjacency matrix. Some sharp bounds are obtained for the (Laplacian) spectral radii of connected graphs. As consequences, some (sharp) upper bounds of the Nordhaus-Gaddum type are also obtained for the sum of (Laplacian) spectral radii of a connected graph and its connected complement. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：755 / 770

页数：16

共 23 条

[1] ALARI CY, 1991, GRAPH THEORY COMBINA, P871
[2] Cao DS, 1998, LINEAR ALGEBRA APPL, V270, P1
[3] Cvetkovic Dragos M., 1980, Pure and applied mathematics: a series of monographs and textbooks
[4] Some new bounds on the spectral radius of graphs
Das, KC
Kumar, P
[J]. DISCRETE MATHEMATICS, 2004, 281 (1-3) : 149 - 161
[5] The spectral radius of graphs on surfaces
Ellingham, MN
Zha, XY
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2000, 78 (01) : 45 - 56
[6] SOME EIGENVALUE PROPERTIES IN GRAPHS (CONJECTURES OF GRAFFITI .2.)
FAVARON, O
MAHEO, M
SACLE, JF
[J]. DISCRETE MATHEMATICS, 1993, 111 (1-3) : 197 - 220
[7] FIEDLER M, 1973, CZECH MATH J, V23, P298
[8] Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees
Hong, Y
Zhang, XD
[J]. DISCRETE MATHEMATICS, 2005, 296 (2-3) : 187 - 197
[9] A sharp upper bound of the spectral radius of graphs
Hong, Y
Shu, JL
Fang, KF
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2001, 81 (02) : 177 - 183
[10] de Caen's inequality and bounds on the largest Laplacian eigenvalue of a graph
Li, JS
Pan, YL
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 328 (1-3) : 153 - 160

← 1 2 3 →