On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths
Michel Mollard
Discussiones Mathematicae Graph Theory, Tome 33 (2013), p. 387-394 / Harvested from The Polish Digital Mathematics Library
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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].

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:267582 
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     author = {Michel Mollard},
     title = {On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {33},
     year = {2013},
     pages = {387-394},
     zbl = {1293.05271},
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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) pp. 387-394. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1668/

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