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
相关论文
共 50 条
  • [1] A characterization of graphs with rank 5
    Chang, Gerard J.
    Huang, Liang-Hao
    Yeh, Hong-Gwa
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (11) : 4241 - 4250
  • [2] A characterization of signed planar graphs with rank at most 4
    Tian, Fenglei
    Wang, Dengyin
    Zhu, Min
    LINEAR & MULTILINEAR ALGEBRA, 2016, 64 (05) : 807 - 817
  • [3] A characterization of long graphs of arbitrary rank
    Wong, Dein
    Zhu, Min
    Lv, Wenping
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (03) : 1347 - 1355
  • [4] Characterization of sub-long graphs of arbitrary rank
    Wang, Long
    Ma, Xiaobin
    LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (07) : 1427 - 1445
  • [5] On the rank of weighted graphs
    Zhang, W. J.
    Yu, A. M.
    LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (03) : 635 - 652
  • [6] The Triangle-Free Graphs with Rank 6
    Long WANG
    Yizheng FAN
    Yi WANG
    JournalofMathematicalResearchwithApplications, 2014, 34 (05) : 517 - 528
  • [7] ON BIPARTITE GRAPHS WHICH ATTAIN MINIMUM RANK AMONG BIPARTITE GRAPHS WITH A GIVEN DIAMETER
    Li, Hong-Hai
    Su, Li
    Sun, Hui-Xian
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2012, 23 : 137 - 150
  • [8] On triangle-free graphs with rank 7
    Duan, Fang
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2025, 56 (01) : 295 - 304
  • [9] On triangle-free graphs with rank 7
    Duan, Fang
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023, : 295 - 304
  • [10] On connected signed graphs with rank equal to girth
    Wu, Qi
    Lu, Yong
    Tam, Bit-Shun
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 651 : 90 - 115
12345