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How To Count Trees?

Author

Listed:
  • 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)

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.

Suggested Citation

  • Sebastian Piec & Krzysztof Malarz & Krzysztof Kułakowski, 2005. "How To Count Trees?," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(10), pages 1527-1534.
    • Handle: RePEc:wsi:ijmpcx:v:16:y:2005:i:10:n:s0129183105008114
    DOI: 10.1142/S0129183105008114
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    References listed on IDEAS

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    1. Christos Pitelis & Roger Sugden & James R. Wilson, 2006. "Introduction," Chapters, in: Christos Pitelis & Roger Sugden & James R. Wilson (ed.), Clusters and Globalisation, chapter 1, Edward Elgar Publishing.
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