Geodesic
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, pp. 387-394

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Let γ ( C_m□C_n ) be the domination number of the Cartesian product of directed cycles C_m and C_n for m, n ≥ 2. Shaheen [13] and Liu et al. ([11], [12]) determined the value of γ ( C_m□C_n ) when m ≤ 6 and [12] when both m and n ≡ 0 ( 3). In this article we give, in general, the value of γ ( C_m□C_n ) when m ≡ 2( 3) and improve the known lower bounds for most of the remaining cases. We also disprove the conjectured formula for the case m ≡ 0 ( 3) appearing in [12].
Keywords: directed graph, Cartesian product, domination number, directed cycle 
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     author = {Mollard, Michel},
     title = {On the {Domination} of {Cartesian} {Product} of {Directed} {Cycles:} {Results} for {Certain} {Equivalence} {Classes} of {Lengths}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {387--394},
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     year = {2013},
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Mollard, Michel. 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, pp. 387-394. http://geodesic.mathdoc.fr/item/DMGT_2013_33_2_a11/