Nordhaus-Gaddum inequalities for domination in graphs

被引：50
|
作者：
Harary, F
Haynes, TW
机构：
[1] NEW MEXICO STATE UNIV, DEPT COMP SCI, LAS CRUCES, NM 88003 USA
[2] E TENNESSEE STATE UNIV, DEPT MATH, JOHNSON CITY, TN 37614 USA
来源：
DISCRETE MATHEMATICS | 1996年 / 155卷 / 1-3期
关键词：
D O I：
10.1016/0012-365X(94)00373-Q
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A node in a graph G = (V,E) is said to dominate itself and all nodes adjacent to it. A set S subset of V is a dominating set for G if each node in V is dominated by some node in S and is a double dominating set for G if each node in V is dominated by at least two nodes in S. First we give a brief survey of Nordhaus-Gaddum results for several domination-related parameters. Then we present new inequalities of this type involving double domination. A direct result of our bounds for double domination in complementary graphs is a new Nordhaus-Gaddum inequality for open domination improving known bounds for the case when both G and its complement have domination number greater than 4.
引用
收藏
页码：99 / 105
页数：7
相关论文
共 50 条
  • [1] A note on Nordhaus-Gaddum inequalities for domination
    Shan, EF
    Dang, CY
    Kang, LY
    [J]. DISCRETE APPLIED MATHEMATICS, 2004, 136 (01) : 83 - 85
  • [2] NORDHAUS-GADDUM TYPE INEQUALITIES FOR MULTIPLE DOMINATION AND PACKING PARAMETERS IN GRAPHS
    Mojdeh, Doost Ali
    Samadi, Babak
    Volkmann, Lutz
    [J]. CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2020, 15 (01) : 154 - 162
  • [3] Nordhaus-Gaddum type inequalities on the total Italian domination number in graphs
    Sheikholeslami, Seyed Mahmoud
    Volkmann, Lutz
    [J]. RAIRO-OPERATIONS RESEARCH, 2022, 56 (04) : 2235 - 2243
  • [4] PRODUCTS OF GRAPHS AND NORDHAUS-GADDUM TYPE INEQUALITIES
    Keyvan, Nastran
    Rahmati, Farhad
    [J]. TRANSACTIONS ON COMBINATORICS, 2018, 7 (01) : 30 - 35
  • [5] Inequalities of Nordhaus-Gaddum type for doubly connected domination number
    Akhbari, M. H.
    Hasni, R.
    Favaron, O.
    Karami, H.
    Sheikholeslami, S. M.
    [J]. DISCRETE APPLIED MATHEMATICS, 2010, 158 (14) : 1465 - 1470
  • [6] Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs
    Hattingh, Johannes H.
    Jonck, Elizabeth
    Joubert, Ernst J.
    Plummer, Andrew R.
    [J]. DISCRETE MATHEMATICS, 2008, 308 (07) : 1080 - 1087
  • [7] Nordhaus-Gaddum bounds for total domination
    Henning, Michael A.
    Joubert, Ernst J.
    Southey, Justin
    [J]. APPLIED MATHEMATICS LETTERS, 2011, 24 (06) : 987 - 990
  • [8] A Nordhaus-Gaddum bound for Roman domination
    Rad, Nader Jafari
    Rahbani, Hadi
    [J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2019, 11 (05)
  • [9] Nordhaus-Gaddum bounds for independent domination
    Goddard, W
    Henning, MA
    [J]. DISCRETE MATHEMATICS, 2003, 268 (1-3) : 299 - 302
  • [10] Nordhaus-Gaddum problems for power domination
    Benson, Katherine F.
    Ferrero, Daniela
    Flagg, Mary
    Furst, Veronika
    Hogben, Leslie
    Vasilevska, Violeta
    [J]. DISCRETE APPLIED MATHEMATICS, 2018, 251 : 103 - 113
12345