How to count trees?

Int. J. Mod. Phys. C16 (2005) 1527 We propose a new topological invariant of unlabeled trees of N nodes. The invariant is a set of Nx2 matrices of integers, with sum_j k^{d_{i,j}} and v_i as the matrix elements, where d_{i,j} are the elements of the distance matrix and v_i denotes i-th node's d...

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Bibliographic Details
Main Authors Piec, S, Malarz, K, Kulakowski, K
Format Journal Article
LanguageEnglish
Published 25.01.2005
Subjects
Physics - Statistical Mechanics
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Summary:Int. J. Mod. Phys. C16 (2005) 1527 We propose a new topological invariant of unlabeled trees of N nodes. The invariant is a set of Nx2 matrices of integers, with sum_j k^{d_{i,j}} and v_i as the matrix elements, where d_{i,j} are the elements of the distance matrix and v_i denotes i-th node's degree and k in N. To compare the invariant calculated for possibly different graphs, the matrix rows are ordered with respect to 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 to N=17. The results slightly exceed the asymptotic evaluation of Otter.
DOI:10.48550/arxiv.cond-mat/0501594