Number of Dominating Sets in Cylindric Square Grid Graphs

被引：0
|
作者：
Seungsang Oh
机构：
[1] Korea University,Department of Mathematics
来源：
Graphs and Combinatorics | 2021年 / 37卷
关键词：
Domination polynomial; Dominating set; Cylindric square grid; 05A15; 05C69;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A dominating set of a graph is a subset D of the vertices such that every vertex not in D is adjacent to some vertex of D. In this paper, we introduce several variants of dominating sets in the square grid, periodic square grid and cylindric square grid by considering translation symmetry. We provide their exact enumerations in terms of domination polynomials. We also analyze the asymptotic behavior of the growth rates of their cardinality.
引用
收藏
页码：1357 / 1372
页数：15
相关论文
共 50 条
  • [41] Uniform clutters and dominating sets of graphs
    Marti-Farre, Jaume
    Mora, Merce
    Luis Ruiz, Jose
    DISCRETE APPLIED MATHEMATICS, 2019, 263 : 220 - 233
  • [42] Distributed Dominating Sets in Interval Graphs
    Gorain, Barun
    Mondal, Kaushik
    Pandit, Supantha
    COMPUTING AND COMBINATORICS, COCOON 2022, 2022, 13595 : 508 - 520
  • [43] On dominating sets of maximal outerplanar graphs
    Campos, C. N.
    Wakabayashi, Y.
    DISCRETE APPLIED MATHEMATICS, 2013, 161 (03) : 330 - 335
  • [44] Independent dominating sets in regular graphs
    Haviland, Julie
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2013, 26 (01) : 120 - 126
  • [45] Constructing Dominating Sets in Circulant Graphs
    Shparlinski, Igor E.
    ANNALS OF COMBINATORICS, 2018, 22 (01) : 201 - 211
  • [46] Double hop dominating sets in graphs
    Mollejon, Reynaldo, V
    Canoy, Sergio R., Jr.
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2021, 13 (05)
  • [47] DOMINATING SETS IN SOCIAL NETWORK GRAPHS
    KELLEHER, LL
    COZZENS, MB
    MATHEMATICAL SOCIAL SCIENCES, 1988, 16 (03) : 267 - 279
  • [48] INTERIOR TOTAL DOMINATING SETS IN GRAPHS
    Pacardo, Shiela Mae B.
    Rara, Helen M.
    ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2018, 19 (04): : 373 - 390
  • [49] Properties of partial dominating sets of graphs
    Case, Benjamin M.
    Fenstermacher, Todd
    Ganguly, Soumendra
    Laskar, Renu C.
    arXiv, 2019,
  • [50] END SUPER DOMINATING SETS IN GRAPHS
    Akbari, Saieed
    Ghanbari, Nima
    Henning, Michael A.
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2023,
12345