On the domination number of Cartesian product of two directed cycles
type: Item
instance of: scholarly article
title: On the domination number of Cartesian product of two directed cycles
zbMATH Open document ID: 1397.05135
DOI: 10.1155/2013/619695
author: Zehui Shao
author: Fangnian Lang
author: Enqiang Zhu
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: Denote by \(\gamma(G)\) the domination number of a digraph \(G\) and \(C_m\square C_n\) the Cartesian product of \(C_m\) and \(C_n\), the directed cycles of length \(m,n\geq 2\). In [Inf. Process. Lett. 110, No. 5, 171--173 (2010; Zbl 1197.05111)], \textit{J. Liu} et al. determined the exact values of \(\gamma(C_m\square C_n)\) for \(m=2,3,4,5,6\). In [Discuss. Math., Graph Theory 33, No. 2, 387--394 (2013; Zbl 1293.05271)], \textit{M. Mollard} determined the exact values of \(\gamma(C_m\square C_n)\) for \(m=3k+2\). In this paper, we give lower and upper bounds of \(\gamma(C_m\square C_n)\) with \(m=3k+1\) for different cases. In particular, \(\lceil (2k+1)n/2\rceil\leq\gamma(C_{3k+1}\square C_n)\leq \lfloor(2k+1)n/2 \rfloor+k\). Based on the established result, the exact values of \(\gamma(C_m\square C_n)\) are determined for \(m=7\) and 10 by the combination of the dynamic algorithm, and an upper bound for \(\gamma(C_{13}\square C_n)\) is provided.
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 6950782
Wikidata QID: Q59003353
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/619695
OpenAlex ID: W2074608221
description: scientific article; zbMATH DE number 6950782