T-Code (in a graph)

[math]\displaystyle{ t }[/math]-Code (in a graph) --- [math]\displaystyle{ t }[/math]-код (в графе).

A set [math]\displaystyle{ C \subseteq V(G) }[/math] is a [math]\displaystyle{ t }[/math]-code in [math]\displaystyle{ G }[/math] if [math]\displaystyle{ d(u,v) \geq 2t+1 }[/math] for any two distinct vertices [math]\displaystyle{ u,v \in C }[/math]; [math]\displaystyle{ t }[/math]-codes are known as [math]\displaystyle{ 2t }[/math]-packings. In addition, [math]\displaystyle{ C }[/math] is called a [math]\displaystyle{ t }[/math]-perfect code if for any [math]\displaystyle{ u \in V(G) }[/math] there is exactly one [math]\displaystyle{ v \in C }[/math] such that [math]\displaystyle{ d(u,v) \leq t }[/math]; 1-perfect codes are also called efficient dominating sets.

A set [math]\displaystyle{ C \subseteq V(G) }[/math] is a 1-perfect code if and only if the closed neigbourhoods of its elements form a partition of [math]\displaystyle{ V(G) }[/math].