- Tytuł:
- On locating and differentiating-total domination in trees
- Autorzy:
- Chellali, Mustapha
- Powiązania:
- https://bibliotekanauki.pl/articles/743043.pdf
- Data publikacji:
- 2008
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
locating-total domination
differentiating-total domination
trees - Opis:
- A total dominating set of a graph G = (V,E) with no isolated vertex is a set S ⊆ V such that every vertex is adjacent to a vertex in S. A total dominating set S of a graph G is a locating-total dominating set if for every pair of distinct vertices u and v in V-S, N(u)∩S ≠ N(v)∩S, and S is a differentiating-total dominating set if for every pair of distinct vertices u and v in V, N[u]∩S ≠ N[v] ∩S. Let $γₜ^L(G)$ and $γₜ^D(G)$ be the minimum cardinality of a locating-total dominating set and a differentiating-total dominating set of G, respectively. We show that for a nontrivial tree T of order n, with l leaves and s support vertices, $γₜ^L(T) ≥ max{2(n+l-s+1)/5,(n+2-s)/2}$, and for a tree of order n ≥ 3, $γₜ^D(T) ≥ 3(n+l-s+1)/7$, improving the lower bounds of Haynes, Henning and Howard. Moreover we characterize the trees satisfying $γₜ^L(T) = 2(n+l- s+1)/5$ or $γₜ^D(T) = 3(n+l-s+1)/7$.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2008, 28, 3; 383-392
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł