More results on the domination number of Cartesian product of two directed cycles

Ye, Ansheng (author), Miao, Fang (author), Shao, Zehui (author), Liu, Jia-Bao (author), Žerovnik, Janez (author), Repolusk, Polona (author)

Let γ(D) denote the domination number of a digraph D and let C$_m$□C$_n$ denote the Cartesian product of C$_m$ and C$_n$, the directed cycles of length n ≥ m ≥ 3. Liu et al. obtained the exact values of γ(C$_m$□C$_n$) for m up to 6 [Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36–39]. Shao et al. determined the exact values of γ(C$_m$□C$_n$) for m = 6, 7 [On the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 619695]. Mollard obtained the exact values of γ(C$_m$□C$_n$) for m = 3k + 2 [M. Mollard, On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths, Discuss. Math. Graph Theory 33(2) (2013) 387–394.]. In this paper, we extend the current known results on C$_m$□C$_n$ with m up to 21. Moreover, the exact values of γ(C$_n$□C$_n$) with n up to 31 are determined.

• Language: English
• Keywords: domination number, Cartesian product, directed cycle
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2019
• Number of pages: 9 str.
• Numbering: Vol. 7, iss. 2, art. 210
• PID: 20.500.12556/RUL-131962
• UDC: 519.1
• ISSN on article: 2227-7390
• DOI: 10.3390/math7020210
• COBISS.SI-ID: 24462088
• Publication date in RUL: 07.10.2021

Record is a part of a journal

• Title: Mathematics
• Shortened title: Mathematics
• Publisher: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
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• Licensing start date: 24.02.2019