- Tytuł:
- A note on global alliances in trees
- Autorzy:
-
Bouzefrane, M.
Chellali, M. - Powiązania:
- https://bibliotekanauki.pl/articles/254977.pdf
- Data publikacji:
- 2011
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
global defensive alliance
global offensive alliance
domination
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 (respectively, defensive) alliance if for each vertex in V - S (respectively, in S) at least half the vertices from the closed neighborhood of v are in S. The domination number γ (G) is the minimum cardinality of a dominating set of G, and the global offensive alliance number γo(G) (respectively, global defensive alliance number γa(G)) is the minimum cardinality of a global offensive alliance (respectively, global deffensive alliance) of G. We show that if T is a tree of order n, then γo(T) ≤ 2γ (T) - 1 and if n ≥ 3, then γo(T) ≤ 3/2?a(T) ? 1. Moreover, all extremal trees attaining the first bound are characterized.
- Źródło:
-
Opuscula Mathematica; 2011, 31, 2; 153-159
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł