On spectral integral variations of graphs

被引：26

作者：

Fan, YZ ^{[1
]}

机构：

[1] Anhui Univ, Dept Math, Hefei 230039, Anhui, Peoples R China

[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2002年 / 50卷 / 02期

关键词：

spectrum; spectral integral variation; Laplacian integral; matrix-tree theorem; M-matrix;

D O I：

10.1080/03081080290019513

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a general graph. The spectrum S(G) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e. We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge.

引用

页码：133 / 142

页数：10

共 9 条

[1]

Alavi Y., 1991, Graph theory, combinatorics, and applications, V2, P871

[2]

Anderson W. N., 1985, Linear Multilinear Algebra, V18, P141, DOI [10.1080/03081088508817681, DOI 10.1080/03081088508817681]

[3]

[Anonymous], 1979, NONNEGATIVE MATRICES

[4]

Cvetkovic D. M., 1982, Spectra of graphs. Theory and application, VSecond

[5] LOWER BOUNDS FOR THE 1ST EIGENVALUE OF CERTAIN M-MATRICES ASSOCIATED WITH GRAPHS [J].

FRIEDLAND, S .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 172 :71-84

[6] On the second real eigenvalue of nonnegative and Z-matrices [J].

Friedland, S ;

Nabben, R .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 255 :303-313

[7]

Horn R. A., 1986, Matrix analysis

[8] DEGREE MAXIMAL GRAPHS ARE LAPLACIAN INTEGRAL [J].

MERRIS, R .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1994, 199 :381-389

[9]

So W., 1999, LINEAR MULTILINEAR A, V46, P193

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