- Tytuł:
- On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths
- Autorzy:
- Mollard, Michel
- Powiązania:
- https://bibliotekanauki.pl/articles/30146581.pdf
- Data publikacji:
- 2013-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
directed graph
Cartesian product
domination number
directed cycle - Opis:
- Let \( \gamma ( \overrightarrow{C_m} \square \overrightarrow{C_n} ) \) be the domination number of the Cartesian product of directed cycles \( \overrightarrow{C_m} \) and \( \overrightarrow{C_n} \) for $m, n \ge 2 $. Shaheen [13] and Liu et al. ([11], [12]) determined the value of \( \gamma ( \overrightarrow{C_m} \square \overrightarrow{C_n} ) \) when $ m \le 6 $ and [12] when both $m$ and $ n \equiv 0 (\mod 3) $. In this article we give, in general, the value of \( \gamma ( \overrightarrow{C_m} \square \overrightarrow{C_n} ) \) when $ m \equiv 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 \equiv 0 ( \mod 3) $ appearing in [12].
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2013, 33, 2; 387-394
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł