Lower Bounds on the (Laplacian) Spectral Radius of Weighted Graphs

被引：3
作者：
Yu, Aimei [1 ]
Lu, Mei [2 ]
机构：
[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2014年 / 35卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Weighted graphs; Adjacency matrix; Laplacian matrix; Spectral radius; Lower bounds; SHARP UPPER; LARGEST EIGENVALUE; MATRICES;
D O I：
10.1007/s11401-014-0840-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.
引用
收藏
页码：669 / 678
页数：10
相关论文
共 50 条
  • [41] Upper bounds of spectral radius of symmetric matrices and graphs
    Jin, Ya-Lei
    Zhang, Jie
    Zhang, Xiao-Dong
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2024, 682 : 152 - 163
  • [42] Some sharp upper bounds on the spectral radius of graphs
    Feng, Lihua
    Li, Qiao
    Zhang, Xiao-Dong
    [J]. TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (04): : 989 - 997
  • [43] Bounds for the spectral radius of the Aa-matrix of graphs
    Alhevaz, Abdollah
    Baghipur, Maryam
    Ganie, Hilal Ahmad
    [J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2024, 55 (01) : 298 - 309
  • [44] On the signless Laplacian spectral radius of irregular graphs
    Ning, Wenjie
    Li, Hao
    Lu, Mei
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (05) : 2280 - 2288
  • [45] On the distance Laplacian spectral radius of bicyclic graphs
    Xu, Nannan
    Yu, Aimei
    Hao, Rong-Xia
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (19) : 4654 - 4674
  • [46] The vertex bipartiteness and the Laplacian spectral radius of graphs
    Jia, Huicai
    Xue, Jie
    [J]. ARS COMBINATORIA, 2020, 151 : 57 - 62
  • [47] Graphs with maximal signless Laplacian spectral radius
    Chang, Ting-Jung
    Tam, Bit-Shun
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (07) : 1708 - 1733
  • [48] The Laplacian spectral radius of graphs with given connectivity
    Feng, Lihua
    Ilic, Aleksandar
    [J]. ARS COMBINATORIA, 2012, 104 : 489 - 495
  • [49] The signless Laplacian spectral radius of graphs on surfaces
    Feng, Lihua
    Yu, Guihai
    Ilic, Aleksandar
    Stevanovic, Dragan
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (05) : 573 - 581
  • [50] Maximizing the signless Laplacian spectral radius of graphs with given diameter or cut vertices
    Wang, Jianfeng
    Huang, Qiongxiang
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (07) : 733 - 744
12345