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
  • [41] Upper bounds on the domination number of a graph in terms of order and minimum degree
    Volkmann, Lutz
    ARS COMBINATORIA, 2006, 81 : 3 - 22
  • [42] Upper Bounds on the k-Tuple (Roman) Domination Number of a Graph
    Michael A. Henning
    Nader Jafari Rad
    Graphs and Combinatorics, 2021, 37 : 325 - 336
  • [43] Improved Bounds on the k-tuple (Roman) Domination Number of a Graph
    Noor A’lawiah Abd Aziz
    Michael A. Henning
    Nader Jafari Rad
    Hailiza Kamarulhaili
    Graphs and Combinatorics, 2022, 38
  • [44] Bounds On k-Part Degree Restricted Domination Number Of A Graph
    Kamath, Shyam S.
    Thilak, A. Senthil
    Maladi, Rashmi
    APPLIED MATHEMATICS E-NOTES, 2021, 21 : 139 - 151
  • [45] On a relation between the domination number and a strongly connected bidirection of an undirected graph
    Laetsch, Martin
    Peis, Britta
    DISCRETE APPLIED MATHEMATICS, 2008, 156 (17) : 3194 - 3202
  • [46] Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
    Lemanska, Magdalena
    Alberto Rodriguez-Velazquez, Juan
    Trujillo-Rasua, Rolando
    FUNDAMENTA INFORMATICAE, 2017, 152 (03) : 273 - 287
  • [47] On the domination number of a graph
    Pruchnewski, A
    DISCRETE MATHEMATICS, 2002, 251 (1-3) : 129 - 136
  • [48] THE INDEPENDENT DOMINATION NUMBER OF A CUBIC 3-CONNECTED GRAPH CAN BE MUCH LARGER THAN ITS DOMINATION NUMBER
    KOSTOCHKA, AV
    GRAPHS AND COMBINATORICS, 1993, 9 (03) : 235 - 237
  • [49] Bounds on the strong domination number
    Rautenbach, D
    DISCRETE MATHEMATICS, 2000, 215 (1-3) : 201 - 212
  • [50] Bounds on the domination number of a digraph
    Hao, Guoliang
    Qian, Jianguo
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2018, 35 (01) : 64 - 74
12345