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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| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
25-01-2005
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| Subjects: | |
| Online Access: | Get full text |
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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. |
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| DOI: | 10.48550/arxiv.cond-mat/0501594 |