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Number of Dominating Sets in Cylindric Square Grid Graphs
- Authors
- Oh, Seungsang
- Issue Date
- 7월-2021
- Publisher
- SPRINGER JAPAN KK
- Keywords
- Cylindric square grid; Dominating set; Domination polynomial
- Citation
- GRAPHS AND COMBINATORICS, v.37, no.4, pp.1357 - 1372
- Indexed
- SCIE
SCOPUS
- Journal Title
- GRAPHS AND COMBINATORICS
- Volume
- 37
- Number
- 4
- Start Page
- 1357
- End Page
- 1372
- ISSN
- 0911-0119
- Abstract
- 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.
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