On the global offensive alliance in unicycle graphs

Abstract

For a graph , a set is a dominating set if every vertex in has at least a neighbor in . A dominating set is a global offensive alliance if for each vertex in at least half the vertices from the closed neighborhood of are in The domination number is the minimum cardinality of a dominating set of , and the global offensive alliance number is the minimum cardinality of a global offensive alliance of . We show that if is a connected unicycle graph of order with leaves and support vertices then . Moreover, we characterize all extremal unicycle graphs attaining this bound.

Keywords

• domination
• global offensive alliance
• unicycle graph