On the Domination Number of Cartesian Product of Two Directed Cycles

Zehui Shao, Enqiang Zhu and Fangnian Lang

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: Denote by γ(G) the domination number of a digraph G and Cm□Cn the Cartesian product of Cm and Cn, the directed cycles of length m, n ≥ 2. In 2010, Liu et al. determined the exact values of γ(Cm□Cn) for m = 2,3, 4,5, 6. In 2013, Mollard determined the exact values of γ(Cm□Cn) for m = 3k + 2. In this paper, we give lower and upper bounds of γ(Cm□Cn) with m = 3k + 1 for different cases. In particular, ⌈(2k + 1)n/2⌉≤γ(C3k+1□Cn)≤⌊(2k + 1)n/2⌋+k. Based on the established result, the exact values of γ(Cm□Cn) are determined for m = 7 and 10 by the combination of the dynamic algorithm, and an upper bound for γ(C13□C n) is provided.

Date: 2013
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https://doi.org/10.1155/2013/619695

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:619695

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