دورية أكاديمية
Further results on the total Italian domination number of trees
| العنوان: | Further results on the total Italian domination number of trees |
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| المؤلفون: | Abel Cabrera-Martínez, Andrea Conchado Peiró, Juan Manuel Rueda-Vázquez |
| المصدر: | AIMS Mathematics, Vol 8, Iss 5, Pp 10654-10664 (2023) |
| بيانات النشر: | AIMS Press |
| سنة النشر: | 2023 |
| المجموعة: | Directory of Open Access Journals: DOAJ Articles |
| مصطلحات موضوعية: | total italian domination number, double domination number, domination number, trees, Mathematics, QA1-939 |
| الوصف: | Let $ f:V(G)\rightarrow \{0, 1, 2\} $ be a function defined from a connected graph $ G $. Let $ W_i = \{x\in V(G): f(x) = i\} $ for every $ i\in \{0, 1, 2\} $. The function $ f $ is called a total Italian dominating function on $ G $ if $ \sum_{v\in N(x)}f(v)\geq 2 $ for every vertex $ x\in W_0 $ and if $ \sum_{v\in N(x)}f(v)\geq 1 $ for every vertex $ x\in W_1\cup W_2 $. The total Italian domination number of $ G $, denoted by $ \gamma_{tI}(G) $, is the minimum weight $ \omega(f) = \sum_{x\in V(G)}f(x) $ among all total Italian dominating functions $ f $ on $ G $. In this paper, we provide new lower and upper bounds on the total Italian domination number of trees. In particular, we show that if $ T $ is a tree of order $ n(T)\geq 2 $, then the following inequality chains are satisfied. (ⅰ) $ 2\gamma(T)\leq \gamma_{tI}(T)\leq n(T)-\gamma(T)+s(T) $, (ⅱ) $ \frac{n(T)+\gamma(T)+s(T)-l(T)+1}{2}\leq \gamma_{tI}(T)\leq \frac{n(T)+\gamma(T)+l(T)}{2}, $ where $ \gamma(T) $, $ s(T) $ and $ l(T) $ represent the classical domination number, the number of support vertices and the number of leaves of $ T $, respectively. The upper bounds are derived from results obtained for the double domination number of a tree. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| تدمد: | 2473-6988 |
| العلاقة: | https://doaj.org/toc/2473-6988Test; https://doaj.org/article/1658ac6328f44e37bfec8d951caf6737Test |
| DOI: | 10.3934/math.2023540 |
| الإتاحة: | https://doi.org/10.3934/math.2023540Test https://doaj.org/article/1658ac6328f44e37bfec8d951caf6737Test |
| رقم الانضمام: | edsbas.298BE2C9 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 24736988 |
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| DOI: | 10.3934/math.2023540 |