On the (Laplacian) spectral radius of bipartite graphs with given number of blocks

被引：0

作者：

Zhai, Mingqing ^{[1
,2
]}

Liu, Ruifang ^{[1
]}

Shu, Jinlong ^{[1
]}

机构：

[1] Chuzhou Univ, Dept Math, Chuzhou 239012, Anhui, Peoples R China

[2] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

来源：

ARS COMBINATORIA | 2011年 / 98卷

关键词：

Bipartite graph; Block; Spectral radius; Laplacian spectral radius; K-PENDANT VERTICES; LARGEST EIGENVALUE; SHARP UPPER; MATRICES; DIAMETER; TREES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The (Laplacian) spectral radius of a graph is the maximum eigenvalue of its adjacency matrix (Laplacian matrix, respectively). Let G(n, k) be the set of bipartite graphs with n vertices and k blocks. This paper gives a complete characterization for the extremal graph with the maximum spectral radius (Laplacian spectral radius, respectively) in G(n, k).

引用

页码：311 / 319

页数：9

共 13 条

[1] On the spectral radius of graphs with cut vertices [J].

Berman, A ;

Zhang, XD .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2001, 83 (02) :233-240

[2] ON THE SPECTRAL-RADIUS OF COMPLEMENTARY ACYCLIC MATRICES OF ZEROS AND ONES [J].

BRUALDI, RA ;

SOLHEID, ES .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1986, 7 (02) :265-272

[3]

Cvetkovic D., 1995, Spectra of Graphs: Theory and Applications

[4] The spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices [J].

Guo, SG .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 408 :78-85

[5] Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees [J].

Hong, Y ;

Zhang, XD .

DISCRETE MATHEMATICS, 2005, 296 (2-3) :187-197

[6] On the spectral radius of graphs with cut edges [J].

Liu, HQ ;

Lu, M ;

Tian, F .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 389 :139-145

[7]

MERRIS R, 1994, LINEAR ALGEBRA APPL, V198, P143

[8] A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph [J].

Shu, JL ;

Hong, Y ;

Wen-Ren, K .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 347 (1-3) :123-129

[9] Graphs with given diameter maximizing the spectral radius [J].

van Dam, E. R. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 426 (2-3) :454-457

[10] The spectral radius of trees on k pendant vertices [J].

Wu, BF ;

Xiao, E ;

Hong, Y .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 395 :343-349

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