The Laplacian spectrum of a mixed graph

被引：36
作者：
Zhang, XD
Li, JS
机构：
[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200030, Peoples R China
[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2002年 / 353卷
关键词：
mixed graph; Laplacian matrix; line graph; spectrum;
D O I：
10.1016/S0024-3795(01)00538-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we discuss some properties of relations between a mixed graph and its line graph, which are used to characterize the Laplacian spectrum of a mixed graph. Then we present two sharp upper bounds for the Laplacian spectral radius of a mixed graph in terms of the degrees and the average 2-degrees of vertices and we also determine some extreme graphs which attain these upper bounds. (C) 2002 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：11 / 20
页数：10
相关论文
共 12 条
  • [1] [Anonymous], 1979, NONNEGATIVE MATRICES
  • [2] [Anonymous], LINEAR ALGEBRA APPL
  • [3] Edge version of the matrix tree theorem for trees
    Bapat, RB
    Grossman, JW
    Kulkarni, D
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2000, 47 (03) : 217 - 229
  • [4] Bapat RB., 1999, Linear Multilinear Algebra, V46, P299, DOI DOI 10.1080/03081089908818623
  • [5] BERMAN A, 2001, J COMB THEORY B, V83, P183
  • [6] Bondy J.A., 2008, GRAD TEXTS MATH
  • [7] ALGEBRAIC GRAPH-THEORY WITHOUT ORIENTATION
    GROSSMAN, JW
    KULKARNI, DM
    SCHOCHETMAN, IE
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1994, 212 : 289 - 307
  • [8] Li JS, 1997, LINEAR ALGEBRA APPL, V265, P93
  • [9] Mel'nikov LS, 1999, J GRAPH THEOR, V31, P267, DOI 10.1002/(SICI)1097-0118(199908)31:4<267::AID-JGT1>3.0.CO
  • [10] 2-D
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