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

2020/02/19 by José Aliste‐Prieto, Aliste-Prieto, José, Anna de Mier +3
Chemistry · Mathematics · Physics and Astronomy · #05C31 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2002.08186

openalex publication_date 2020/02/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this article, we construct explicit examples of pairs of non-isomorphic\ntrees with the same restricted U-polynomial for every k; by this we mean\nthat the polynomials agree on terms with degree at most k+1. The main tool\nfor this construction is a generalization of the U-polynomial to rooted\ngraphs, which we introduce and study in this article. Most notably we show that\nrooted trees can be reconstructed from its rooted U-polynomial.\n

Citations

• On an Algorithm for Comparing the Chromatic Symmetric Functions of Trees
• Chromatic symmetric functions via the group algebra of S_n

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