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 neighbourhoods of its elements form a partition of [math]\displaystyle{ \,V(G) }[/math].

Литература

• Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.