Connected global offensive k-alliances in graphs
Lutz Volkmann · Discussiones Mathematicae Graph Theory · 2011
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 subseto (G) is the minimum cardinality of a connected global offensive k-alliance in G.In this paper we characterize connected graphs G with γ k,c o (G) = n(G).In the case that δ(G) ≥ k ≥ 2, we also characterize the family of connected graphs G with γ k,c o (G) = n(G)-1.Furthermore, we present different tight bounds of γ k,c o (G).