On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths
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 (−→...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2013-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1668 |
| _version_ | 1797757788358705152 |
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| author | Mollard Michel |
| author_facet | Mollard Michel |
| author_sort | Mollard Michel |
| collection | DOAJ |
| description | 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]. |
| first_indexed | 2024-03-12T18:20:33Z |
| format | Article |
| id | doaj.art-ce51636cd90e434299ba1e5d99461985 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T18:20:33Z |
| publishDate | 2013-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-ce51636cd90e434299ba1e5d994619852023-08-02T08:58:21ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922013-05-0133238739410.7151/dmgt.1668On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of LengthsMollard Michel0CNRS Université Joseph Fourier Institut Fourier 100, rue des Maths 38402 St Martin d’Hères Cedex FranceLet (−→ 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].https://doi.org/10.7151/dmgt.1668directed graphcartesian productdomination numberdirected cycle |
| spellingShingle | Mollard Michel On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths Discussiones Mathematicae Graph Theory directed graph cartesian product domination number directed cycle |
| title | On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths |
| title_full | On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths |
| title_fullStr | On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths |
| title_full_unstemmed | On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths |
| title_short | On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths |
| title_sort | on the domination of cartesian product of directed cycles results for certain equivalence classes of lengths |
| topic | directed graph cartesian product domination number directed cycle |
| url | https://doi.org/10.7151/dmgt.1668 |
| work_keys_str_mv | AT mollardmichel onthedominationofcartesianproductofdirectedcyclesresultsforcertainequivalenceclassesoflengths |