Bounds on the connected domination number of a graph

被引：20
|
作者：
Desormeaux, Wyatt J. [1 ]
Haynes, Teresa W. [1 ,2 ]
Henning, Michael A. [1 ]
机构：
[1] Univ Johannesburg, Dept Math, ZA-2006 Auckland Pk, South Africa
[2] E Tennessee State Univ, Dept Math & Stat, Johnson City, TN 37614 USA
来源：
DISCRETE APPLIED MATHEMATICS | 2013年 / 161卷 / 18期
基金：
新加坡国家研究基金会;
关键词：
Connected domination; Girth; Domination;
D O I：
10.1016/j.dam.2013.06.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A subset S of vertices in a graph G = (V, E) is a connected dominating set of G if every vertex of V\S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number gamma(c)(G) The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then gamma(c) (G) >= g(G) - 2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus-Gaddum type results. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：2925 / 2931
页数：7
相关论文
共 50 条
  • [21] New Probabilistic Upper Bounds on the Domination Number of a Graph
    Rad, Nader Jafari
    ELECTRONIC JOURNAL OF COMBINATORICS, 2019, 26 (03):
  • [22] Some bounds for the signed edge domination number of a graph
    Akbari, S.
    Esfandiari, H.
    Barzegary, E.
    Seddighin, S.
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2014, 58 : 60 - 66
  • [23] Upper Bounds on the Paired Domination Subdivision Number of a Graph
    Yoshimi Egawa
    Michitaka Furuya
    Masanori Takatou
    Graphs and Combinatorics, 2013, 29 : 843 - 856
  • [24] Upper bounds on the signed edge domination number of a graph
    Dong, Fengming
    Ge, Jun
    Yang, Yan
    DISCRETE MATHEMATICS, 2021, 344 (02)
  • [25] Upper bounds for the Roman domination subdivision number of a graph
    Khodkar, Abdollah
    Mobaraky, B.
    Sheikholeslami, S.
    AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2008, 5 (01) : 7 - 14
  • [26] Upper Bounds on the Paired Domination Subdivision Number of a Graph
    Egawa, Yoshimi
    Furuya, Michitaka
    Takatou, Masanori
    GRAPHS AND COMBINATORICS, 2013, 29 (04) : 843 - 856
  • [27] Bounds on the Distance Two-Domination Number of a Graph
    N. Sridharan
    V.S.A. Subramanian
    M.D. Elias
    Graphs and Combinatorics, 2002, 18 : 667 - 675
  • [28] BOUNDS FOR THE m-ETERNAL DOMINATION NUMBER OF A GRAPH
    Henning, Michael A.
    Klostermeyer, William F.
    Macgillivray, Gary
    CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2017, 12 (02) : 91 - 103
  • [29] A note on the lower bounds of signed domination number of a graph
    Zhang, ZF
    Xu, BG
    Li, YZ
    Liu, LZ
    DISCRETE MATHEMATICS, 1999, 195 (1-3) : 295 - 298
  • [30] Bounds on the distance two-domination number of a graph
    Sridharan, N
    Subramanian, VSA
    Elias, MD
    GRAPHS AND COMBINATORICS, 2002, 18 (03) : 667 - 675
12345