Bounds on Laplacian eigenvalues related to total and signed domination of graphs

被引：0
|
作者：
Wei Shi
Liying Kang
Suichao Wu
机构：
[1] Shanghai Sanda University,Department of Mathematics
[2] Shanghai University,School of Fundamentel Studies
[3] Shanghai University of Engineering Science,undefined
来源：
Czechoslovak Mathematical Journal | 2010年 / 60卷
关键词：
algebraic connectivity; Laplacian matrix; Laplacian spectral radius; signed domination; total domination; 05C50; 05C69;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A total dominating set in a graph G is a subset X of V (G) such that each vertex of V (G) is adjacent to at least one vertex of X. The total domination number of G is the minimum cardinality of a total dominating set. A function f: V (G) → {−1, 1} is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of an SDF is the sum of its function values over all vertices. The signed domination number of G is the minimum weight of an SDF on G. In this paper we present several upper bounds on the algebraic connectivity of a connected graph in terms of the total domination and signed domination numbers of the graph. Also, we give lower bounds on the Laplacian spectral radius of a connected graph in terms of the signed domination number of the graph.
引用
收藏
页码：315 / 325
页数：10
相关论文
共 50 条
  • [1] Bounds on Laplacian eigenvalues related to total and signed domination of graphs
    Shi, Wei
    Kang, Liying
    Wu, Suichao
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2010, 60 (02) : 315 - 325
  • [2] Signed (total) domination numbers and Laplacian spectrum of graphs
    Ghameshlou, A. N.
    Sheikholeslami, S. M.
    JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2009, 12 (01): : 93 - 99
  • [3] The k-Domination Number and Bounds for the Laplacian Eigenvalues of Graphs
    Li, Rao
    UTILITAS MATHEMATICA, 2009, 79 : 189 - 192
  • [4] BOUNDS ON THE INVERSE SIGNED TOTAL DOMINATION NUMBERS IN GRAPHS
    Atapour, M.
    Norouzian, S.
    Sheikholeslami, S. M.
    Volkmann, L.
    OPUSCULA MATHEMATICA, 2016, 36 (02) : 145 - 152
  • [5] NEW BOUNDS ON THE SIGNED TOTAL DOMINATION NUMBER OF GRAPHS
    Mochaddam, Seyyed Mehdi Hosseini
    Mojdeh, Doost Ali
    Samadi, Babak
    Volkmann, Lutz
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2016, 36 (02) : 467 - 477
  • [6] On the Laplacian eigenvalues of signed graphs
    Hou, YP
    Li, JS
    Pan, YL
    LINEAR & MULTILINEAR ALGEBRA, 2003, 51 (01): : 21 - 30
  • [7] LOWER BOUNDS ON SIGNED EDGE TOTAL DOMINATION NUMBERS IN GRAPHS
    Karami, H.
    Sheikholeslami, S. M.
    Khodkar, Abdollah
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2008, 58 (03) : 595 - 603
  • [8] Upper bounds on the upper signed total domination number of graphs
    Shan, Erfang
    Cheng, T. C. E.
    DISCRETE APPLIED MATHEMATICS, 2009, 157 (05) : 1098 - 1103
  • [9] Bounds on the signed total Roman 2-domination in graphs
    Khoeilar, R.
    Shahbazi, L.
    Sheikholeslami, S. M.
    Shao, Zehui
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2020, 12 (01)
  • [10] Lower bounds on signed edge total domination numbers in graphs
    H. Karami
    S. M. Sheikholeslami
    Abdollah Khodkar
    Czechoslovak Mathematical Journal, 2008, 58 : 595 - 603
12345