F-Stable set

[math]\displaystyle{ f }[/math]-Stable set --- [math]\displaystyle{ f }[/math]-устойчивое множество.

A set of vertices [math]\displaystyle{ S \subset V(G) }[/math] is said to be an [math]\displaystyle{ f }[/math]-stable set, if [math]\displaystyle{ d_{G}(u,v) \geq f(u) + f(v) }[/math] holds for each pair of distinct vertices [math]\displaystyle{ u,v \in S }[/math]. If we take a constant function taking the value 1 as [math]\displaystyle{ f }[/math], an [math]\displaystyle{ f }[/math]-stable set is an ordinary stable set (also called an independent set). The [math]\displaystyle{ f }[/math]-stability number, denoted by [math]\displaystyle{ \alpha_{f}(G) = \max\{|S|: \; S\mbox{ is an {\it f}-stable set}\} }[/math].