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 12 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 SEM HAMBURG, V21, P63, DOI [DOI 10.1007/BF02941924, 10.1007/BF02941924]

[3]

CVEKOVIC DM, 1980, SPECTRA GRAPHS

[4]

CVETKOVIC D, 1972, CROAT CHEM ACTA, V44, P365

[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 and the matching number of unicyclic graphs [J].

Guo, Ji-Ming ;

Yan, Weigen ;

Yeh, Yeong-Nan .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (08) :1293-1301

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

Li, Shuchao .

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

[9] SOME STUDIES IN MOLECULAR ORBITAL THEORY .1. RESONANCE STRUCTURES AND MOLECULAR ORBITALS IN UNSATURATED HYDROCARBONS [J].

LONGUETHIGGINS, HC .

JOURNAL OF CHEMICAL PHYSICS, 1950, 18 (03) :265-274

[10]

Schwenk A.J., 1978, Selected Topics in Graph Theory, P307

← 1 2 →