Global strong alliance number

Global strong alliance number --- число глобального строгого альянса.

A global strong defensive alliance in a graph [math]\displaystyle{ G = (V,E) }[/math] is a dominating set [math]\displaystyle{ S }[/math] of [math]\displaystyle{ G }[/math] satisfying the condition that, for every vertex [math]\displaystyle{ v \in S }[/math], the number of neighbors [math]\displaystyle{ v }[/math] has in [math]\displaystyle{ S }[/math] is at least as large as the number of neighbors it has in [math]\displaystyle{ V - S }[/math]. The global strong alliance number is the minimum cardinality of a global strong defensive alliance in [math]\displaystyle{ G }[/math].