Graphs whose normalized Laplacian has three eigenvalues

被引：27

作者：

van Dam, E. R. ^{[1
]}

Omidi, G. R. ^{[2
,3
]}

机构：

[1] Tilburg Univ, Dept Econometr & Operat Res, NL-5000 LE Tilburg, Netherlands

[2] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

[3] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 10期

关键词：

Normalized Laplacian matrix; Transition matrix; Graph spectra; Eigenvalues; Strongly regular graphs; Quasi-symmetric designs; STRONGLY REGULAR GRAPHS;

D O I：

10.1016/j.laa.2011.02.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic families of examples from conference graphs, projective planes, and certain quasi-symmetric designs. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2560 / 2569

页数：10

共 26 条

[1]

[Anonymous], LINEAR MULT IN PRESS

[2]

[Anonymous], 2007, CRC HDB COMBINATORIA

[3]

[Anonymous], ARXIV10083646V1

[4]

Bridges W.G., 1981, Aequationes Mathematicae, V22, P208

[5] A note about cospectral graphs for the adjacency and normalized Laplacian matrices [J].

Butler, Steve .

LINEAR & MULTILINEAR ALGEBRA, 2010, 58 (03) :387-390

[6] On the normalized Laplacian energy and general Randic index R_1 of graphs [J].

Cavers, Michael ;

Fallat, Shaun ;

Kirkland, Steve .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (01) :172-190

[7] An interlacing result on normalized Laplacians [J].

Chen, GT ;

Davis, G ;

Hall, F ;

Li, ZS ;

Patel, K ;

Stewart, M .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2004, 18 (02) :353-361

[8] Graphs with three distinct eigenvalues and largest eigenvalue less than 8 [J].

Chuang, H. ;

Omidi, G. R. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (8-9) :2053-2062

[9]

Chung F., 1997, CBMS Lecture Notes

[10]

Cvetkovec D.M., 1995, SPECTRA GRAPHS THEOR, Vthird

← 1 2 3 →