Bounds on the Global Offensive K-Alliance Number in Graphs
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 ΙN(ν) ∩ SΙ ≥ ΙN(ν)-SΙ+k for every ν ε V (G)-S, where N(v) is the neighborhood of ν. The global offensive k-alliance number γko(G) is the minimum cardinality of a global o ensive k-alliance in G. We present di erent bounds on γko(G) in terms of order, maximum degree, independence number, chromatic number and minimum degree.
Chellali, Mustapha; Haynes, Teresa W.; Randerath, Bert; and Volkmann, Lutz. 2009. Bounds on the Global Offensive K-Alliance Number in Graphs. Discussiones Mathematicae - Graph Theory. Vol.29(3). 597-613. https://doi.org/10.7151/dmgt.1467 ISSN: 1234-3099