English

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 UU-polynomial for every kk; by this we mean that the polynomials agree on terms with degree at most k+1k+1. The main tool for this construction is a generalization of the UU-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 UU-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}
}
R2 v1 2026-06-23T13:46:49.576Z