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Diskretnyi Analiz i Issledovanie Operatsii, 2023, Volume 30, Issue 1, Pages 110–129
DOI: https://doi.org/10.33048/daio.2023.30.745 (Mi da1318) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the number of minimum total dominating sets in trees

D. S. Taletskiiab

a Lobachevsky Nizhny Novgorod State University, 23 Gagarin Street, 603950 Nizhny Novgorod, Russia
b National Research University “Higher School of Economics”, 25/12 Bolshaya Pechyorskaya Street, 603155 Nizhny Novgorod, Russia
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DOI: https://doi.org/10.33048/daio.2023.30.745
Abstract: The minimum total dominating set (MTDS) of a graph is a vertex subset $D$ of minimum cardinality such that every vertex of the graph is adjacent to at least one vertex of $D.$ In this paper we obtain the sharp upper bound for the number of MTDS in the class of $n$-vertex $2$-caterpillars. We also show that for all $n \geq 1$ every $n$-vertex tree has less than $(\sqrt{2})^n$ MTDS. Illustr. 5, bibliogr. 6.
Keywords: extremal combinatorics, tree, $2$-caterpillar, minimum total dominating set.
Funding agency Grant number
Russian Science Foundation 21-11-00194
This research was supported by the Russian Science Foundation, project no. 21-11-00194.
Received: 16.06.2022
Revised: 04.10.2022
Accepted: 06.10.2022
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 1, Pages 213–224
DOI: https://doi.org/10.1134/S1990478923010234
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: D. S. Taletskii, “On the number of minimum total dominating sets in trees”, Diskretn. Anal. Issled. Oper., 30:1 (2023), 110–129; J. Appl. Industr. Math., 17:1 (2023), 213–224
Citation in format AMSBIB
\Bibitem{Tal23}
\by D.~S.~Taletskii
\paper On the number of minimum total dominating~sets~in~trees
\jour Diskretn. Anal. Issled. Oper.
\yr 2023
\vol 30
\issue 1
\pages 110--129
\mathnet{http://mi.mathnet.ru/da1318}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4569860}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 1
\pages 213--224
\crossref{https://doi.org/10.1134/S1990478923010234}
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