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On the Domination Number of Cartesian Product of Two Directed Cycles

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  • Zehui Shao
  • Enqiang Zhu
  • Fangnian Lang

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.

Suggested Citation

  • Zehui Shao & Enqiang Zhu & Fangnian Lang, 2013. "On the Domination Number of Cartesian Product of Two Directed Cycles," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:619695
    DOI: 10.1155/2013/619695
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    References listed on IDEAS

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    1. Kelleher, Laura L. & Cozzens, Margaret B., 1988. "Dominating sets in social network graphs," Mathematical Social Sciences, Elsevier, vol. 16(3), pages 267-279, December.
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