On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 387.

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Let (−→ Cm2−→ 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 (−→ Cm2−→ Cn) when m ≤ 6 and [12] when both m and n ≡ 0(mod 3). In this article we give, in general, the value of (−→ Cm2−→ 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].
Classification : 05C20, 05C38, 05C69, 05C76
Mots-clés : directed graph, Cartesian product, domination number, directed cycle 
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Michel Mollard. On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 387. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_267582/