Székely, L. A.; Wang, Hua Binary trees with the largest number of subtrees. (English) Zbl 1113.05025 Discrete Appl. Math. 155, No. 3, 374-385 (2007). 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. Cited in 3 ReviewsCited in 28 Documents MSC: 05C05 Trees 05C12 Distance in graphs 05C30 Enumeration in graph theory Keywords:Wiener index Citations:Zbl 1009.05052; Zbl 0993.05061 Software:OEIS PDFBibTeX XMLCite \textit{L. A. Székely} and \textit{H. Wang}, Discrete Appl. Math. 155, No. 3, 374--385 (2007; Zbl 1113.05025) Full Text: DOI Online Encyclopedia of Integer Sequences: Maximum number of nonempty subtrees of a binary tree with n leaves. 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.