Offensive r-alliances in graphs

Abstract

a b s t r a c tLet G = (V , E) be a simple graph. For a nonempty set X ⊂ V , and a vertex vthe boundary of S. An offensive ralliance S is called global if it forms a dominating set. The global offensive r-alliance number of G, denoted by γ o r (G), is the minimum cardinality of a global offensive r-alliance in G. Weshow that the problem of finding optimal (global) offensive r-alliances is NP-complete and we obtain several tight bounds on γ o r (G).

Bounds on the global offensive k-alliance number in graphs

“…A global offensive 1-alliance is a global offensive alliance and a global offensive 2-alliance is a global strong offensive alliance. In [7], Fernau, Rodríguez and Sigarreta show that the problem of finding optimal global offensive k-alliances is N P -complete.…”