Abstract
Abstract An offensive alliance in a graph Γ = ( V , E ) is a set of vertices S ⊂ V where for every vertex v in its boundary it holds that the majority of vertices in v 's closed neighborhood are in S . In the case of strong offensive alliance, strict majority is required. An alliance S is called global if it affects every vertex in V S , that is, S is a dominating set of Γ. The global offensive alliance number γ o ( Γ ) (respectively, global strong offensive alliance number γ o ˆ ( Γ ) ) is the minimum cardinality of a global offensive (respectively, global strong offensive) alliance in Γ. In this paper we obtain several tight bounds on γ o ( Γ ) and γ o ˆ ( Γ ) in terms of several parameters of Γ.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
