K-Restricted total domination number

[math]\displaystyle{ k }[/math]-Restricted total domination number --- число [math]\displaystyle{ k }[/math]-ограниченного тотального доминирования.

The [math]\displaystyle{ k }[/math]-restricted total domination number of a graph [math]\displaystyle{ G }[/math] is the smallest integer [math]\displaystyle{ r_{k}(G,\gamma_{t}) }[/math] such that, given any subset [math]\displaystyle{ U }[/math] of [math]\displaystyle{ k }[/math] vertices of [math]\displaystyle{ G }[/math], there exists a total dominating set of [math]\displaystyle{ G }[/math] of cardinality at most [math]\displaystyle{ r_{k}(G,\gamma_{t}) }[/math] containing [math]\displaystyle{ U }[/math]. Hence, the [math]\displaystyle{ k }[/math]-restricted total domination number of a graph [math]\displaystyle{ G }[/math] measures how many vertices are necessary to totally dominate a graph if an arbitrary set of [math]\displaystyle{ k }[/math] vertices must be included in the total dominating set. When [math]\displaystyle{ k = 0 }[/math], the [math]\displaystyle{ k }[/math]-restricted total domination number is the total domination number.