- Tytuł:
- On the global offensive alliance number of a tree
- Autorzy:
-
Bouzefrane, M.
Chellali, M. - Powiązania:
- https://bibliotekanauki.pl/articles/255263.pdf
- Data publikacji:
- 2009
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
global offensive alliance number
domination number
trees - Opis:
- For a graph G = (V, E), a set S ⊆ V is a dominating set if every vertex in V - S has at least a neighbor in S. A dominating set S is a global offensive alliance if for every vertex v in V - S, at least half of the vertices in its closed neighborhood are in S. The domination number ϒ(G) is the minimum cardinality of a dominating set of G and the global offensive alliance number ϒo(G) is the minimum cardinality of a global offensive alliance of G. We first show that every tree of order at least three with l leaves and s support vertices satisfies ϒo(T) ≥ (n - l + s + 1)/3 and we characterize extremal trees attaining this lower bound. Then we give a constructive characterization of trees with equal domination and global offensive alliance numbers.
- Źródło:
-
Opuscula Mathematica; 2009, 29, 3; 223-228
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki