HOW TO COUNT TREES?

Sebastian Piec, Krzysztof Malarz () and Krzysztof Kułakowski
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Sebastian Piec: AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, PL-30059 Kraków, Poland
Krzysztof Malarz: AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, PL-30059 Kraków, Poland
Krzysztof Kułakowski: AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, PL-30059 Kraków, Poland

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 10, 1527-1534

Abstract: We propose a new topological invariant of unlabeled trees ofNnodes. The invariant is a set ofN×2matrices of integers, with∑jkdi, jandvias the matrix elements, wheredi, jare the elements of the distance matrix andvidenotesith node's degree andk∈ℕ. To compare the invariant calculated for possibly different graphs, the matrix rows are ordered with respect to the first column, and, if necessary, with respect to the second one. We use the new invariant to evaluate from below the number of topologically different unlabeled trees up toN =17. The results slightly exceed the asymptotic evaluation of Otter.

Keywords: Computer modeling and simulation; trees and graphs (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0129183105008114

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