Bounds on the global offensive k-alliance number in graphs
Mustapha Chellali, Teresa W. Haynes, Bert Randerath, Lutz Volkmann (2009)
Discussiones Mathematicae Graph Theory
Similarity:
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 is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on in terms of order, maximum degree, independence number, chromatic number and minimum degree.