Connected global offensive k-alliances in graphs
Lutz Volkmann
Discussiones Mathematicae Graph Theory, Tome 31 (2011), p. 699-707 / Harvested from The Polish Digital Mathematics Library
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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 γₒk,c(G) is the minimum cardinality of a connected global offensive k-alliance in G. In this paper we characterize connected graphs G with γₒk,c(G)=n(G). In the case that δ(G) ≥ k ≥ 2, we also characterize the family of connected graphs G with γₒk,c(G)=n(G)-1. Furthermore, we present different tight bounds of γₒk,c(G).

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:270888 
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Lutz Volkmann. Connected global offensive k-alliances in graphs. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 699-707. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1574/

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