- Tytuł:
- A New Upper Bound for the Perfect Italian Domination Number of a Tree
- Autorzy:
-
Nazari-Moghaddam, Sakineh
Chellali, Mustapha - Powiązania:
- https://bibliotekanauki.pl/articles/32304138.pdf
- Data publikacji:
- 2022-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Italian domination
Roman domination
perfect Italian domination - Opis:
- A perfect Italian dominating function (PIDF) on a graph $G$ is a function $ f : V (G) \rightarrow \{ 0, 1, 2 \} $ satisfying the condition that for every vertex u with $f(u) = 0$, the total weight of $f$ assigned to the neighbors of $u$ is exactly two. The weight of a PIDF is the sum of its functions values over all vertices. The perfect Italian domination number of $G$, denoted $ \gamma_I^p (G) $, is the minimum weight of a PIDF of $G$. In this paper, we show that for every tree $T$ of order $ n \ge 3 $, with $ \mathcal{l} (T) $ leaves and $s(T)$ support vertices, \( \gamma_I^p (T) \ge \tfrac {4n- \mathscr{l}(T) + 2s (T) - 1}{5} \), improving a previous bound given by T.W. Haynes and M.A. Henning in [Perfect Italian domination in trees, Discrete Appl. Math. 260 (2019) 164–177].
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 1005-1022
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł