Geodesic
On trees with given diameter and extremal number of distance-$k$ independent sets
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 111-131.

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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 $k \geq 1.$ 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 $1 k d \leq 5.$ The minimum problem is significantly more simple and is solved for all $1 k d n.$ Illustr. 4, bibliogr. 10.
Keywords: tree, independent set, distance-$k$ independent set, diameter. 
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D. S. Taletskii. On trees with given diameter and extremal number of distance-$k$ independent sets. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 111-131. http://geodesic.mathdoc.fr/item/DA_2023_30_3_a5/

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