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Discussiones Mathematicae Graph Theory 33(2) (2013)
387-394
DOI: https://doi.org/10.7151/dmgt.1668
On the domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths
Michel Mollard
CNRS Université Joseph Fourier |
Abstract
Let γ(Cm→□Cn→) be the domination number of the Cartesian product of directed cycles Cm→ and Cn→ for m,n ≥ 2. Shaheen [13] and Liu et al. ([11], [12]) determined the value of γ(Cm→□Cn→) when m ≤ 6 and [12] when both m and n ≡ 0 (mod 3). In this article we give, in general, the value of γ(Cm→□Cn→) when m ≡ 2(mod 3) and improve the known lower bounds for most of the remaining cases. We also disprove the conjectured formula for the case m ≡ 0(mod 3) appearing in [12].
Keywords: directed graph, Cartesian product, domination number, directed cycle
2010 Mathematics Subject Classification: 05C69,05C38.
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Received 8 April 2011
Revised 24 May 2012
Accepted 28 May 2012
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