On 2-domination and 2-rainbow domination of cylindrical graphsOn 2-domination and 2-rainbow domination of cylindrical graphs...J. Žerovnik

被引：0
|
作者：
Janez Žerovnik [1 ]
机构：
[1] University of Ljubljana,FME
[2] Rudolfovo - Science and Technology Centre Novo Mesto,undefined
来源：
Computational and Applied Mathematics | 2025年 / 44卷 / 5期
关键词：
2-domination; Weak 2-domination; Singleton 2-rainbow domination; Cylindrical graphs; 305C69; 05C76;
D O I：
10.1007/s40314-025-03201-2
中图分类号：
学科分类号：
摘要：
Cylindrical graphs and torus grid graphs are naturally constructed from subgraphs of the infinite grid by certain identifications of boundary vertices. Considering various domination type problems, it is usually possible to find an optimal solution on the infinite grid. To the contrary, exact values of invariants for the cylindrical and torus grid graphs are typically only known for special subfamilies, and are in general hard to compute. The 2-domination and 2-rainbow domination of cylindrical graphs is studied, and some new formulae and improved bounds are reported. We also consider weak 2-domination and singleton rainbow domination.
引用
收藏
相关论文
共 50 条
  • [1] On the 2-rainbow domination in graphs
    Bresar, Bostjan
    Sumenjak, Tadeja Kraner
    DISCRETE APPLIED MATHEMATICS, 2007, 155 (17) : 2394 - 2400
  • [2] On 2-rainbow domination and Roman domination in graphs
    Chellali, Mustapha
    Rad, Nader Jafari
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2013, 56 : 85 - 93
  • [3] A note on stratified domination and 2-rainbow domination in graphs
    Aldemir, Mehmet Serif
    Ediz, Suleyman
    JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS, 2011, 13 (7-8): : 833 - 836
  • [4] A note on total domination and 2-rainbow domination in graphs
    Furuya, Michitaka
    DISCRETE APPLIED MATHEMATICS, 2015, 184 : 229 - 230
  • [5] Note on 2-rainbow domination and Roman domination in graphs
    Wu, Yunjian
    Xing, Huaming
    APPLIED MATHEMATICS LETTERS, 2010, 23 (06) : 706 - 709
  • [6] Averaging 2-rainbow domination and Roman domination
    Alvarado, Jose D.
    Dantas, Simone
    Rautenbach, Dieter
    DISCRETE APPLIED MATHEMATICS, 2016, 205 : 202 - 207
  • [7] 2-Rainbow domination stability of graphs
    Li, Zepeng
    Shao, Zehui
    Xu, Shou-jun
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2019, 38 (03) : 836 - 845
  • [8] On the 2-rainbow domination stable graphs
    Li, Zepeng
    Shao, Zehui
    Wu, Pu
    Zhao, Taiyin
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2019, 37 (04) : 1327 - 1341
  • [9] Total 2-Rainbow Domination in Graphs
    Jiang, Huiqin
    Rao, Yongsheng
    MATHEMATICS, 2022, 10 (12)
  • [10] On the 2-rainbow domination stable graphs
    Zepeng Li
    Zehui Shao
    Pu Wu
    Taiyin Zhao
    Journal of Combinatorial Optimization, 2019, 37 : 1327 - 1341
12345