ON THE CHARACTERIZATION OF GRAPHS WITH PENDENT VERTICES AND GIVEN NULLITY

被引：0

作者：

Liu, Bolian ^{[1
]}

Huang, Yufei ^{[1
]}

Chen, Siyuan ^{[1
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2009年 / 18卷

关键词：

Eigenvalue; Nullity; Pendent vertex;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a graph with n vertices. The nullity of G, denoted by eta(G), is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we characterize the graphs (resp. bipartite graphs) with pendent vertices and nullity eta, where 0 < eta <= n. Moreover, the minimum (resp. maximum) number of edges for all (connected) graphs with pendent vertices and nullity eta are determined, and the extremal graphs are characterized.

引用

页码：719 / 734

页数：16

共 50 条

[31] Remarks on the nullity of graphs
Ghorbani, Modjtaba
Songhori, Mahin
UTILITAS MATHEMATICA, 2016, 101 : 139 - 147
[32] A Characterization of Bicyclic Signed Graphs with Nullity n-7
Guojun LI
Aimei YU
Journal of Mathematical Research with Applications, 2015, 35 (01) : 1 - 10
[33] Maximizing the signless Laplacian spectral radius of graphs with given diameter or cut vertices
Wang, Jianfeng
Huang, Qiongxiang
LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (07) : 733 - 744
[34] Bounds of nullity for complex unit gain graphs
Chen, Qian-Qian
Guo, Ji-Ming
LINEAR ALGEBRA AND ITS APPLICATIONS, 2024, 699 : 569 - 585
[35] Minimum energy on trees with k pendent vertices
Yu, Aimei
Lv, Xuezheng
LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (2-3) : 625 - 633
[36] On the nullity of graphs with pendant trees
Gong, Shi-Cai
Fan, Yi-Zheng
Yin, Zhi-Xiang
LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (07) : 1374 - 1380
[37] The number of P-vertices in a matrix with maximum nullity
Fernandes, Rosario
da Cruz, Henrique F.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 547 : 168 - 182
[38] A Note on the Nullity of Unicyclic Graphs
Wei ZHU
Journal of Mathematical Research with Applications, 2010, (05) : 817 - 824
[39] The nullity of bicyclic signed graphs
Fan, Yi-Zheng
Du, Wen-Xue
Dong, Chun-Long
LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (02) : 242 - 251
[40] On the nullity of a family of tripartite graphs
Farooq, Rashid
Malik, Mehar Ali
Naureen, Qudsia
Pirzada, Shariefuddin
ACTA UNIVERSITATIS SAPIENTIAE INFORMATICA, 2016, 8 (01) : 96 - 107

← 1 2 3 4 5 →