A characterization of spectral integral variation in two places for Laplacian matrices

被引：14

作者：

Kirkland, S ^{[1
]}

机构：

[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

LINEAR & MULTILINEAR ALGEBRA | 2004年 / 52卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1080/0308108031000122506

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the graphs having the property that adding a particular edge will result in exactly two Laplacian eigenvalues increasing by I and the other Laplacian eigenvalues remaining fixed. For a certain subclass of graphs, we also characterize the Laplacian integral graphs with that property. Finally, we investigate a situation in which the algebraic connectivity is one of the eigenvalues that increases by I.

引用

页码：79 / 98

页数：20

共 11 条

[1]

[Anonymous], 1976, GRAPH THEORY APPL

[2]

[Anonymous], LINEAR ALGEBRA APPL

[3]

Brualdi R. A., 1991, COMBINATORIAL MATRIX, V39

[4] Spectral integral variations of degree maximal graphs [J].

Fan, YZ .

LINEAR & MULTILINEAR ALGEBRA, 2003, 51 (02) :147-154

[5] On spectral integral variations of graphs [J].

Fan, YZ .

LINEAR & MULTILINEAR ALGEBRA, 2002, 50 (02) :133-142

[6]

FIEDLER M, 1973, CZECH MATH J, V23, P298

[7]

Horn R. A., 1986, Matrix analysis

[8] A bound on the algebraic connectivity of a graph in terms of the number of cutpoints [J].

Kirkland, S .

LINEAR & MULTILINEAR ALGEBRA, 2000, 47 (01) :93-103

[9] On graphs with equal algebraic and vertex connectivity [J].

Kirkland, SJ ;

Molitierno, JJ ;

Neumann, M ;

Shader, BL .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 341 (1-3) :45-56

[10] LAPLACE EIGENVALUES OF GRAPHS - A SURVEY [J].

MOHAR, B .

DISCRETE MATHEMATICS, 1992, 109 (1-3) :171-183

← 1 2 →