- Tytuł:
- Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
- Autorzy:
-
Rad, Nader Jafari
Rahbani, Hadi - Powiązania:
- https://bibliotekanauki.pl/articles/31342324.pdf
- Data publikacji:
- 2018-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
locating-dominating set
differentiating-total dominating set
tree - Opis:
- A subset $S$ of vertices in a graph $G = (V,E)$ is a dominating set of $G$ if every vertex in $V − S$ has a neighbor in $S$, and is a total dominating set if every vertex in $V$ has a neighbor in $S$. A dominating set $S$ is a locating-dominating set of $G$ if every two vertices $ x, y \in V − S$ satisfy $N(x) \cap S \ne N(y) \cap S$. The locating-domination number $ \gamma_L (G) $ is the minimum cardinality of a locating-dominating set of $G$. A total dominating set $S$ is called a differentiating-total dominating set if for every pair of distinct vertices $u$ and $v$ of $G$, $ N[u] \cap S \ne N[v] \cap S $. The minimum cardinality of a differentiating-total dominating set of $G$ is the differentiating-total domination number of $G$, denoted by $ \gamma_t^D (G) $. We obtain new upper bounds for the locating-domination number, and the differentiating-total domination number in trees. Moreover, we characterize all trees achieving equality for the new bounds.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 455-462
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł