Graphs whose distance matrix has at most three negative eigenvalues

被引:0
作者
Tian, Fenglei [1 ]
Wong, Dein [1 ]
机构
[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Peoples R China
关键词
Distance matrix; D-eigenvalue; Negative inertia; INERTIA; SPECTRA; ENERGY;
D O I
10.1016/j.laa.2017.05.040
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let D(G) be the distance matrix of a connected simple graph G. The negative inertia of D(G), denoted by n(D)(G), is the number of negative eigenvalues of D(G). In this paper, we determine all connected graphs G whose distance matrix D(G) has at most three negative eigenvalues. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码:470 / 484
页数:15
相关论文
共 19 条
  • [1] Distance spectra of graphs: A survey
    Aouchiche, Mustapha
    Hansen, Pierre
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 458 : 301 - 386
  • [2] COMPUTER-GENERATION OF DISTANCE POLYNOMIALS OF GRAPHS
    BALASUBRAMANIAN, K
    [J]. JOURNAL OF COMPUTATIONAL CHEMISTRY, 1990, 11 (07) : 829 - 836
  • [3] On distance matrices and Laplacians
    Bapat, R
    Kirkland, SJ
    Neumann, M
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 401 : 193 - 209
  • [4] Brouwer AE, 2012, UNIVERSITEXT, P1, DOI 10.1007/978-1-4614-1939-6
  • [5] A characterization of graphs with rank 4
    Chang, Gerard J.
    Huang, Liang-Hao
    Yeh, Hong-Gwa
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (08) : 1793 - 1798
  • [6] On the nullity of graphs
    Cheng, Bo
    Liu, Bolian
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2007, 16 : 60 - 67
  • [7] Cvetkovie D. M., 1988, RECENT RESULTS THEOR
  • [8] ADDRESSING PROBLEM FOR LOOP SWITCHING
    GRAHAM, RL
    POLLAK, HO
    [J]. BELL SYSTEM TECHNICAL JOURNAL, 1971, 50 (08): : 2495 - +
  • [9] Haynsworth E. V., 1968, LINEAR ALGEBRA APPL, V1, P73, DOI [10.1016/0024-3795(68)90050-5, DOI 10.1016/0024-3795(68)90050-5]
  • [10] The inertia and energy of the distance matrix of a connected graph
    Lin, Huiqiu
    Liu, Ruifang
    Lu, Xiwen
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 467 : 29 - 39