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We investigate the relationship between global offensive k-alliances and some characteristic sets of a graph including r-dependent sets, τ-dominating sets and standard dominating sets. In addition, we discuss the close relationship that exist among the (global) offensive k i-alliance number of Γ i , i ∈ {1, 2} and the (global) offensive k-alliance number of… (More)

A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global)… (More)

- Springer-Verlag Berlin, Heidelberg, Ismael G Yero, Sergio Bermudo, Juan A Rodríguez-Vel´azquez, José M Sigarreta
- 2010

A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global)… (More)