Geodesic
Bounds on the global offensive k-alliance number in graphs
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 597-613

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Let G = (V(G),E(G)) be a graph, and let k ≥ 1 be an integer. A set S ⊆ V(G) is called a global offensive k-alliance if |N(v)∩S| ≥ |N(v)-S|+k for every v ∈ V(G)-S, where N(v) is the neighborhood of v. The global offensive k-alliance number γₒ^k(G) is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on γₒ^k(G) in terms of order, maximum degree, independence number, chromatic number and minimum degree.
Keywords: global offensive k-alliance number, independence number, chromatic number 
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     title = {Bounds on the global offensive k-alliance number in graphs},
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Chellali, Mustapha; Haynes, Teresa; Randerath, Bert; Volkmann, Lutz. Bounds on the global offensive k-alliance number in graphs. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 597-613. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a10/