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

• Autorzy: Michel Mollard
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

directed graph; Cartesian product; domination number; directed cycle

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 387-394

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

Michel Mollard

• CNRS Université Joseph Fourier Institut Fourier 100, rue des Maths 38402 St Martin d’Hères Cedex France

Bibliografia

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• [11] J. Liu, X.D. Zhang, X. Chenand and J. Meng, On domination number of Cartesian product of directed cycles, Inform. Process. Lett. 110 (2010) 171-173. doi:10.1016/j.ipl.2009.11.005[Crossref]
• [12] J. Liu, X.D. Zhang, X. Chen and J. Meng, Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36-39. doi:10.1016/j.ipl.2010.10.001[Crossref]
• [13] R.S. Shaheen, Domination number of toroidal grid digraphs, Util. Math. 78 (2009) 175-184.

Identyfikatory

DOI

10.7151/dmgt.1668