N-Dominating set

[math]\displaystyle{ n }[/math]-Dominating set --- [math]\displaystyle{ n }[/math]-доминирующее множество.

A set [math]\displaystyle{ D }[/math] of vertices in a graph [math]\displaystyle{ G }[/math] is defined to be an [math]\displaystyle{ n }[/math]-dominating set of [math]\displaystyle{ G }[/math] if every vertex of [math]\displaystyle{ V(G) - D }[/math] is within distance [math]\displaystyle{ n }[/math] from some vertex of [math]\displaystyle{ D }[/math]. The minimum cardinality among all [math]\displaystyle{ n }[/math]-dominating sets of a graph [math]\displaystyle{ G }[/math] is called the [math]\displaystyle{ n }[/math]-domination number of [math]\displaystyle{ G }[/math] and is denoted by [math]\displaystyle{ \gamma_{n}(G) }[/math], while the maximum cardinality among all minimal [math]\displaystyle{ n }[/math]-dominating sets of a graph [math]\displaystyle{ G }[/math] is called the upper [math]\displaystyle{ n }[/math]-domination number of [math]\displaystyle{ G }[/math] and is devotedly [math]\displaystyle{ \Gamma_{n}(G) }[/math]. A set [math]\displaystyle{ D }[/math] of vertices in a graph [math]\displaystyle{ G }[/math] is called [math]\displaystyle{ n }[/math]-independent if [math]\displaystyle{ d(u,v) \gt n }[/math] for all [math]\displaystyle{ u,v \in D }[/math]. The independent [math]\displaystyle{ n }[/math]-omination number of a [math]\displaystyle{ G }[/math], denoted by [math]\displaystyle{ i_{n}(G) }[/math], is the minimum cardinality among all maximal [math]\displaystyle{ n }[/math]-independent sets of a graph [math]\displaystyle{ G }[/math], while the [math]\displaystyle{ n }[/math]-independence number of [math]\displaystyle{ G }[/math], denoted by [math]\displaystyle{ \beta_{n}(G) }[/math], is the maximum cardinality among all maximal [math]\displaystyle{ n }[/math]-independent sets of a graph [math]\displaystyle{ G }[/math].