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Diskretnyi Analiz i Issledovanie Operatsii, 2023, Volume 30, Issue 3, Pages 111–131
DOI: https://doi.org/10.33048/daio.2023.30.755 (Mi da1330) 		 
On trees with given diameter and extremal number of distance-$k$ independent sets

D. S. Taletskiiab

a National Research University “Higher School of Economics”, 25/12 Bolshaya Pechyorskaya Street, 603155 Nizhny Novgorod, Russia
b Lobachevsky Nizhny Novgorod State University, 23 Gagarin Avenue, 603950 Nizhny Novgorod, Russia
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DOI: https://doi.org/10.33048/daio.2023.30.755
Abstract: 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.
Funding agency Grant number
Russian Science Foundation 21-11-00194
This research is supported by the Russian Science Foundation (Project 21–11–00194).
Received: 20.10.2022
Revised: 02.05.2023
Accepted: 11.05.2023
Document Type: Article
UDC: 519.17
Language: Russian
Citation: D. S. Taletskii, “On trees with given diameter and extremal number of distance-$k$ independent sets”, Diskretn. Anal. Issled. Oper., 30:3 (2023), 111–131
Citation in format AMSBIB
\Bibitem{Tal23}
\by D.~S.~Taletskii
\paper On trees with given diameter and extremal number of distance-$k$ independent sets
\jour Diskretn. Anal. Issled. Oper.
\yr 2023
\vol 30
\issue 3
\pages 111--131
\mathnet{http://mi.mathnet.ru/da1330}
\crossref{https://doi.org/10.33048/daio.2023.30.755}
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