R-Identifying code

[math]\displaystyle{ r }[/math]-Identifying code --- [math]\displaystyle{ r }[/math]-идентифицирующий код.

Consider a connected undirected graph [math]\displaystyle{ G = (V,E) }[/math], a subset of vertices [math]\displaystyle{ C \subseteq V }[/math], and an integer [math]\displaystyle{ r \geq 1 }[/math]; for any vertex [math]\displaystyle{ v \in V }[/math], let [math]\displaystyle{ B_{r}(v) }[/math] denote the ball of radius [math]\displaystyle{ r }[/math] centered at [math]\displaystyle{ v }[/math]. If for all vertices [math]\displaystyle{ v \in V }[/math], the sets [math]\displaystyle{ B_{r}(v) \cap C }[/math] are all nonempty and different, then [math]\displaystyle{ C }[/math] is called an [math]\displaystyle{ r }[/math]-identifying code.