On the smallest trees with the same restricted $U$-polynomial and the rooted $U$-polynomial
Combinatorics
2020-02-20 v1
Abstract
In this article, we construct explicit examples of pairs of non-isomorphic trees with the same restricted -polynomial for every ; by this we mean that the polynomials agree on terms with degree at most . The main tool for this construction is a generalization of the -polynomial to rooted graphs, which we introduce and study in this article. Most notably we show that rooted trees can be reconstructed from its rooted -polynomial.
Keywords
Cite
@article{arxiv.2002.08186,
title = {On the smallest trees with the same restricted $U$-polynomial and the rooted $U$-polynomial},
author = {José Aliste-Prieto and Anna de Mier and José Zamora},
journal= {arXiv preprint arXiv:2002.08186},
year = {2020}
}