A characterization of graphs with rank 4

被引：69
作者：
Chang, Gerard J. [2 ,3 ,4 ]
Huang, Liang-Hao [1 ]
Yeh, Hong-Gwa [1 ]
机构：
[1] Natl Cent Univ, Dept Math, Jhongli 32001, Taoyuan, Taiwan
[2] Natl Taiwan Univ, Dept Math, Taipei 10617, Taiwan
[3] Natl Taiwan Univ, Inst Math Sci, Taipei 10617, Taiwan
[4] Taipei Off, Natl Ctr Theoret Sci, Taipei, Taiwan
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 434卷 / 08期
关键词：
Nullity; Rank; Adjacency matrix; Graph; Spectrum; MOLECULAR-ORBITALS; SINGULAR GRAPHS; NULLITY; TREES;
D O I：
10.1016/j.laa.2010.09.040
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The rank of a graph G is defined to be the rank of its adjacency matrix. In this paper, we consider the following problem: What is the structure of a connected graph with rank 4? This question has not yet been fully answered in the literature, and only some partial results are known. In this paper we resolve this question by completely characterizing graphs G whose adjacency matrix has rank 4. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：1793 / 1798
页数：6
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