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Binary trees with the largest number of subtrees. (English) Zbl 1113.05025

Summary: This paper characterizes binary trees with \(n\) leaves, which have the greatest number of subtrees. These binary trees coincide with those which were shown by M. Fischermann et al. [Discrete Appl. Math. 122, 127–137 (2002; Zbl 0993.05061)] and F. Jelen and E. Triesch [Discrete Appl. Math. 125, 225–233 (2003; Zbl 1009.05052)] to minimize the Wiener index.

MSC:

05C05 Trees
05C12 Distance in graphs
05C30 Enumeration in graph theory

Keywords:

Wiener index

Software:

OEIS
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Full Text: DOI

References:

[1] Fischermann, M.; Hoffmann, A.; Rautenbach, D.; Székely, L. A.; Volkmann, L., Wiener index versus maximum degree in trees, Discrete Appl. Math., 122, 1-3, 127-137 (2002) · Zbl 0993.05061
[2] C. Heuberger, H. Prodinger, On \(\operatorname{Α;} \)-greedy expansions of numbers, \( \langle;\) http://finanz.math.tu-graz.ac.at/\( \sim;\) prodinger/pdffiles/\( \rangle;\).; C. Heuberger, H. Prodinger, On \(\operatorname{Α;} \)-greedy expansions of numbers, \( \langle;\) http://finanz.math.tu-graz.ac.at/\( \sim;\) prodinger/pdffiles/\( \rangle;\). · Zbl 1211.11012
[3] Jelen, F.; Triesch, E., Superdominance order and distance of trees with bounded maximum degree, Discrete Appl. Math., 125, 2-3, 225-233 (2003) · Zbl 1009.05052
[4] B. Knudsen, Optimal Multiple Parsimony Alignment With Affine Gap Cost Using a Phylogenetic Tree, Lecture Notes in Bioinformatics, vol. 2812, Springer, Berlin, 2003, pp. 433-446.; B. Knudsen, Optimal Multiple Parsimony Alignment With Affine Gap Cost Using a Phylogenetic Tree, Lecture Notes in Bioinformatics, vol. 2812, Springer, Berlin, 2003, pp. 433-446.
[5] The On-Line Encyclopedia of Integer Sequences, A \(092781. \langle;\) http://www.research.att.com/\( \sim;\) njas/sequences \(\rangle;\).; The On-Line Encyclopedia of Integer Sequences, A \(092781. \langle;\) http://www.research.att.com/\( \sim;\) njas/sequences \(\rangle;\). · Zbl 1044.11108
[6] Székely, L. A.; Wang, H., On subtrees of trees, Adv. Appl. Math., 34, 138-155 (2005) · Zbl 1153.05019
[7] L.A. Székely, H. Wang, Binary trees with the largest number of subtrees with at least one leaf, Congr. Numer. 177 (2005) 147-169.; L.A. Székely, H. Wang, Binary trees with the largest number of subtrees with at least one leaf, Congr. Numer. 177 (2005) 147-169. · Zbl 1088.05025
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