论文标题
在具有相同限制的$ u $ $ polynomial的最小树木上
On the smallest trees with the same restricted $U$-polynomial and the rooted $U$-polynomial
论文作者
论文摘要
在本文中，我们构建了一对非同构树的明确例子，每$ k $都有相同的受限$ u $ polynomial;通过这种方式，我们的意思是，多项式最多$ k+1 $一致。该构建的主要工具是将$ u $ polynomial对根图的概括，我们在本文中介绍和研究。最值得注意的是，我们表明可以从其植根的$ u $ polynomial中重建生根的树。
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.
