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On the smallest trees with the same restricted $U$-polynomial and the rooted $U$-polynomial

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 نشر من قبل Jos\\'e Aliste-Prieto
 تاريخ النشر 2020
  مجال البحث
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In this article, we construct explicit examples of pairs of non-isomorphic trees with the same restricted $U$-polynomial for every $k$; by this we mean that the polynomials agree on terms with degree at most $k+1$. The main tool for this construction is a generalization of the $U$-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 $U$-polynomial.



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