О деревьях заданного диаметра с экстремальным количеством k-дистанционных независимых множеств
The set of vertices of a graph is called distance-k independent if the distance between any two of its vertices is greater than some integer k ⩾ 1. In this paper we describe n-vertex trees with a given diameter d which have maximum and minimum possible number of distance-k independent sets among all such trees. The maximum problem is solved for the case 1 < k < d ⩽ 5. The minimum problem is significantly more simple and is solved for all 1 < k < d < n.