- Tytuł:
- On Total Domination in the Cartesian Product of Graphs
- Autorzy:
-
Brešar, Boštjan
Hartinger, Tatiana Romina
Kos, Tim
Milanič, Martin - Powiązania:
- https://bibliotekanauki.pl/articles/31342240.pdf
- Data publikacji:
- 2018-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
total domination
Cartesian product
total domination quotient - Opis:
- Ho proved in [A note on the total domination number, Util. Math. 77 (2008) 97–100] that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers. We extend a result of Lu and Hou from [Total domination in the Cartesian product of a graph and $ K_2 $ or $ C_n $, Util. Math. 83 (2010) 313–322] by characterizing the pairs of graphs $G$ and $H$ for which $ \gamma_t (G \square H)=1/2 \gamma_t (G) \gamma_t (H) $, whenever $ \gamma_t (H) = 2 $. In addition, we present an infinite family of graphs $ G_n $ with $ \gamma_t (G_n) = 2n $, which asymptotically approximate equality in $ \gamma_t (G_n \square H_n ) \ge 1/2 \gamma_t (G_n)^2 $.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 4; 963-976
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł