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On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths

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Mollard M.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 2

387-394

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].

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1 Discussiones Mathematicae Graph Theory

1 Mollard M.

1 2013

Wyniki wyszukiwania

On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths