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

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 2, page 387-394
- ISSN: 2083-5892

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topMichel Mollard. "On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths." Discussiones Mathematicae Graph Theory 33.2 (2013): 387-394. <http://eudml.org/doc/267582>.

@article{MichelMollard2013,

abstract = {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].},

author = {Michel Mollard},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {directed graph; Cartesian product; domination number; directed cycle},

language = {eng},

number = {2},

pages = {387-394},

title = {On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths},

url = {http://eudml.org/doc/267582},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Michel Mollard

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

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 2

SP - 387

EP - 394

AB - 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].

LA - eng

KW - directed graph; Cartesian product; domination number; directed cycle

UR - http://eudml.org/doc/267582

ER -

## References

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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] Zbl1259.05134
- [13] R.S. Shaheen, Domination number of toroidal grid digraphs, Util. Math. 78 (2009) 175-184. Zbl1284.05203

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