The nullity of (k-1)-cyclic graphs

被引：10

作者：

Tan, Xuezhong ^{[1
]}

Liu, Bolian ^{[2
]}

机构：

[1] Guangdong Univ Business Studies, Dept Math, Guangzhou 510320, Guangdong, Peoples R China

[2] S China Normal Univ, Dept Math, Guangzhou 510631, Guangdong, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 07期

关键词：

Nullity; Singular graphs; k-Cyclic graph;

D O I：

10.1016/j.laa.2012.11.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A simple connected graph is called a k-cyclic graph provided that the number of edges equals its order plus (k - 1). In this paper, we define a class of (k - 1)-cyclic graph, denoted by Theta(k). The singularity of Theta-graph is studied. Also, the (k - 1)-cyclic graphs that contain Theta-graph as an induced subgraph are paid much attention. We characterize those graphs that have extreme nullities. The results generalize the corresponding theorems on unicyclic and bicyclic graphs. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3144 / 3153

页数：10

共 13 条

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

Cheng, Bo ;

Liu, Bolian .

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

[2]

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

[3]

Cvetkovic D. M., 1980, Spectra of graphs

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

Fan, Yi-Zheng ;

Qian, Ke-Shi .

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

[5] Trees with maximum nullity [J].

Fiorini, S ;

Gutman, I ;

Sciriha, I .

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

[6] On the nullity of a graph with cut-points [J].

Gong, Shi-Cai ;

Xu, Guang-Hui .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (01) :135-142

[7] On the nullity of graphs with pendant trees [J].

Gong, Shi-Cai ;

Fan, Yi-Zheng ;

Yin, Zhi-Xiang .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (07) :1374-1380

[8] On the nullity of line graphs of trees [J].

Gutman, I ;

Sciriha, I .

DISCRETE MATHEMATICS, 2001, 232 (1-3) :35-45

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

Hu, Shengbiao ;

Tan Xuezhong ;

Liu, Bolian .

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

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

Li, Shuchao .

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

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