Number of Dominating Sets in Cylindric Square Grid Graphs

Seungsang Oh

doi:10.1007/s00373-021-02323-8

Number of Dominating Sets in Cylindric Square Grid Graphs

Seungsang Oh^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1357-1372
Number of pages	16
Journal	Graphs and Combinatorics
Volume	37
Issue number	4
DOIs	https://doi.org/10.1007/s00373-021-02323-8
Publication status	Published - 2021 Jul

Bibliographical note

Funding Information:
This work was supported by Institute for Information and communications Technology Planning and Evaluation (IITP) grant funded by the Korea government(MSIT) (No. 2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity).

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.

Keywords

Cylindric square grid
Dominating set
Domination polynomial

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-021-02323-8

Cite this

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note = "Funding Information: This work was supported by Institute for Information and communications Technology Planning and Evaluation (IITP) grant funded by the Korea government(MSIT) (No. 2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity). Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.",

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N2 - 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.

AB - 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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KW - Dominating set

KW - Domination polynomial

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ER -

Number of Dominating Sets in Cylindric Square Grid Graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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