- Tytuł:
- Bounds on the Locating-Total Domination Number in Trees
- Autorzy:
-
Wang, Kun
Ning, Wenjie
Lu, Mei - Powiązania:
- https://bibliotekanauki.pl/articles/31867549.pdf
- Data publikacji:
- 2020-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
tree
total dominating set
locating-total dominating set
locating-total domination number - Opis:
- Given a graph $G = (V, E)$ with no isolated vertex, a subset $S$ of $V$ is called a total dominating set of $G$ if every vertex in $V$ has a neighbor in $S$. A total dominating set $S$ is called a locating-total dominating set if for each pair of distinct vertices $u$ and $v$ in $V \ S, N(u) ∩ S ≠ N(v) ∩ S$. The minimum cardinality of a locating-total dominating set of $G$ is the locating-total domination number, denoted by $γ_t^L(G)$. We show that, for a tree $T$ of order $n ≥ 3$ and diameter $d$, \(\frac{d+1}{2}≤γ_t^L(T)≤n−\frac{d−1}{2}\), and if $T$ has $l$ leaves, $s$ support vertices and $s_1$ strong support vertices, then \(γ_t^L(T)≥max\Big\{\frac{n+l−s+1}{2}−\frac{s+s_1}{4},\frac{2(n+1)+3(l−s)−s_1}{5}\Big\}\). We also characterize the extremal trees achieving these bounds.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 25-34
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł