On the nullity of tricyclic graphs

被引：55

作者：

Cheng, Bo ^{[2
]}

Liu, Bolian ^{[1
]}

机构：

[1] S China Normal Univ, Dept Math, Guangzhou, Guangdong, Peoples R China

[2] Guangdong Univ Foreign Studies, Dept Math & Stat, Sch Informat, Guangzhou, Guangdong, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 434卷 / 08期

关键词：

Graph eigenvalue; Nullity; r-Partite graph; Tricyclic graph;

D O I：

10.1016/j.laa.2011.01.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The nullity of a graph G, denoted by eta (C), is the multiplicity of the eigenvalue zero in its spectrum. It is known that eta(G) <= n - 2 if C is a simple graph on n vertices and G is not isomorphic to nK(1). The extremal graphs attaining the upper bound n - 2 and the second upper bound n - 3 have been obtained. In this paper, the graphs with nullity n - 4 are characterized. Furthermore the tricyclic graphs with maximum nullity are discussed. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1799 / 1810

页数：12

共 9 条

[1]

Bondy J. A., 1976, Graduate Texts in Mathematics, V290

[2] On the nullity of graphs [J].

Cheng, Bo ;

Liu, Bolian .

ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2007, 16 :60-67

[3]

Collatz L., 1957, Abh. Math. Semin. Univ. Hamburg, V21, P63, DOI DOI 10.1007/BF02941924

[4]

Cvetkovic D. M., 1980, Spectra of graphs

[5] On the nullity of bipartite graphs [J].

Fan, Yi-Zheng ;

Qian, Ke-Shi .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (11-12) :2943-2949

[6] Trees with maximum nullity [J].

Fiorini, S ;

Gutman, I ;

Sciriha, I .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 397 (397) :245-251

[7] On the nullity of bicyclic graphs [J].

Hu, Shengbiao ;

Tan Xuezhong ;

Liu, Bolian .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (07) :1387-1391

[8] On the nullity of graphs with pendent vertices [J].

Li, Shuchao .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (07) :1619-1628

[9] On the nullity of unicyclic graphs [J].

Tan, XX ;

Liu, BL .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 408 :212-220

← 1 →