- Tytuł:
- Connected global offensive k-alliances in graphs
- Autorzy:
- Volkmann, Lutz
- Powiązania:
- https://bibliotekanauki.pl/articles/743583.pdf
- Data publikacji:
- 2011
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
alliances in graphs
connected global offensive k-alliance
global offensive k-alliance
domination - Opis:
-
We consider finite graphs G with vertex set V(G). For a subset S ⊆ V(G), we define by G[S] the subgraph induced by S. By n(G) = |V(G) | and δ(G) we denote the order and the minimum degree of G, respectively. Let k be a positive integer. A subset S ⊆ V(G) is a connected global offensive k-alliance of the connected graph G, if G[S] is connected and |N(v) ∩ S | ≥ |N(v) -S | + k for every vertex v ∈ V(G) -S, where N(v) is the neighborhood of v. The connected global offensive k-alliance number $γₒ^{k,c}(G)$ is the minimum cardinality of a connected global offensive k-alliance in G.
In this paper we characterize connected graphs G with $γₒ^{k,c}(G) = n(G)$. In the case that δ(G) ≥ k ≥ 2, we also characterize the family of connected graphs G with $γₒ^{k,c}(G) = n(G) - 1$. Furthermore, we present different tight bounds of $γₒ^{k,c}(G)$. - Źródło:
-
Discussiones Mathematicae Graph Theory; 2011, 31, 4; 699-707
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł