Total Version of the Domination Game

被引：0
|
作者：
Michael A. Henning
Sandi Klavžar
Douglas F. Rall
机构：
[1] University of Johannesburg,Department of Mathematics
[2] University of Ljubljana,Faculty of Mathematics and Physics
[3] University of Maribor,Faculty of Natural Sciences and Mathematics
[4] Institute of Mathematics,Department of Mathematics
[5] Physics and Mechanics,undefined
[6] Furman University,undefined
来源：
Graphs and Combinatorics | 2015年 / 31卷
关键词：
Domination game; Total domination number; 05C57; 91A43; 05C69;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we continue the study of the domination game in graphs introduced by Brešar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.
引用
收藏
页码：1453 / 1462
页数：9
相关论文
共 50 条
  • [1] Total Version of the Domination Game
    Henning, Michael A.
    Klavzar, Sandi
    Rall, Douglas F.
    GRAPHS AND COMBINATORICS, 2015, 31 (05) : 1453 - 1462
  • [2] Trees with equal total domination and game total domination numbers
    Henning, Michael A.
    Rall, Douglas F.
    DISCRETE APPLIED MATHEMATICS, 2017, 226 : 58 - 70
  • [3] TOTAL CONNECTED DOMINATION GAME
    Bujtas, Csilla
    Henning, Michael A.
    Irsic, Vesna
    Klavzar, Sandi
    OPUSCULA MATHEMATICA, 2021, 41 (04) : 453 - 464
  • [4] On the Game Total Domination Number
    Bujtas, Csilla
    GRAPHS AND COMBINATORICS, 2018, 34 (03) : 415 - 425
  • [5] On the Game Total Domination Number
    Csilla Bujtás
    Graphs and Combinatorics, 2018, 34 : 415 - 425
  • [6] Game total domination for cycles and paths
    Dorbec, Paul
    Henning, Michael A.
    Discrete Applied Mathematics, 2016, 208 : 7 - 18
  • [7] Game total domination for cycles and paths
    Dorbec, Paul
    Henning, Michael A.
    DISCRETE APPLIED MATHEMATICS, 2016, 208 : 7 - 18
  • [8] Game total domination critical graphs
    Henning, Michael A.
    Klavzar, Sandi
    Rall, Douglas F.
    DISCRETE APPLIED MATHEMATICS, 2018, 250 : 28 - 37
  • [9] On the total version of the covering Italian domination problem
    Raju, Alfred
    Palagiri, Venkata S. R.
    Yero, Ismael G.
    DISCRETE APPLIED MATHEMATICS, 2024, 358 : 333 - 343
  • [10] On the total version of the covering Italian domination problem
    Department of Computer Science and Engineering, National Institute of Technology Warangal, Telangana, Hanamkonda
    506004, India
    不详
    不详
    Discrete Appl Math, (333-343):
12345