How to count trees?
| dc.creator | Piec, S. | |
| dc.creator | Malarz, K. | |
| dc.creator | Kulakowski, K. | |
| dc.date | 2005-01-25 | |
| dc.date | 2005-04-07 | |
| dc.date.accessioned | 2026-07-07T06:22:33Z | |
| dc.date.available | 2026-07-07T06:22:33Z | |
| dc.description | 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. | |
| dc.description | 13 pages, 5 figures in 67 eps file, elsart | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0501594 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0501594 | |
| dc.identifier | Int. J. Mod. Phys. C16 (2005) 1527 | |
| dc.identifier | doi:10.1142/S0129183105008114 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95943 | |
| dc.subject | Statistical Mechanics | |
| dc.title | How to count trees? | |
| dc.type | text |