A relation between the matching number and Laplacian spectrum of a graph

被引：23
|
作者：
Ming, GJ [1 ]
Wang, TS [1 ]
机构：
[1] Univ Petr Shandong, Dept Math, Shandong 257061, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2001年 / 325卷 / 1-3期
关键词：
maximum matching; matching number; Laplacian spectrum;
D O I：
10.1016/S0024-3795(00)00333-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a graph, its Laplacian matrix is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. In this paper, we generalize a result in (R. Merris, Port. Math.48 (3) 1991) and obtain the following result: Let G be a graph and M(G) be a maximum matching in G. Then the number of edges in M(G) is a lower bound for the number of Laplacian eigenvalues of G exceeding 2. (C) 2001 Elsevier Science Inc. All rights reserved. AMS classification: 05c50.
引用
收藏
页码：71 / 74
页数：4
相关论文
共 50 条
  • [1] A RELATION BETWEEN THE MATCHING NUMBER AND LAPLACIAN SPECTRUM OF A TREE
    FAN Yizheng (Department of Mathematics
    School of Mathematics and Computational Science
    JournalofSystemsScienceandComplexity, 2005, (02) : 174 - 178
  • [2] Relation between the matching number and the second largest distance Laplacian eigenvalue of a graph
    Tian, Fenglei
    Wong, Dein
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 558 : 174 - 185
  • [3] Relation between the nullity of a graph and its matching number
    Zhou, Qi
    Wong, Dein
    Tian, Fenglei
    DISCRETE APPLIED MATHEMATICS, 2022, 313 : 93 - 98
  • [4] The packing number and Laplacian spectrum of a graph
    Wen, Fei
    Huang, Qiongxiang
    Lou, Zhenzhen
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2014, 91 (07) : 1422 - 1427
  • [5] A relation between the Laplacian and signless Laplacian eigenvalues of a graph
    Saieed Akbari
    Ebrahim Ghorbani
    Jack H. Koolen
    Mohammad Reza Oboudi
    Journal of Algebraic Combinatorics, 2010, 32 : 459 - 464
  • [6] A relation between the Laplacian and signless Laplacian eigenvalues of a graph
    Akbari, Saieed
    Ghorbani, Ebrahim
    Koolen, Jack H.
    Oboudi, Mohammad Reza
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2010, 32 (03) : 459 - 464
  • [7] Relation between the Hermitian energy of a mixed graph and the matching number of its underlying graph
    Wei, Wei
    Li, Shuchao
    LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (07): : 1395 - 1410
  • [8] Relation between the skew energy of an oriented graph and its matching number
    Tian, Fenglei
    Wong, Dein
    DISCRETE APPLIED MATHEMATICS, 2017, 222 : 179 - 184
  • [9] A RELATION BETWEEN GROWTH AND THE SPECTRUM OF THE LAPLACIAN
    BROOKS, R
    MATHEMATISCHE ZEITSCHRIFT, 1981, 178 (04) : 501 - 508
  • [10] On the relation between the H-rank of a mixed graph and the matching number of its underlying graph
    Chen, Chen
    Huang, Jing
    Li, Shuchao
    LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (09): : 1853 - 1869
12345