# Rooted trees with the same plucking polynomial

## TL;DR

This paper characterizes when two rooted trees share the same plucking polynomial and provides criteria for sequences of integers to correspond to rooted trees, advancing understanding of tree invariants.

## Contribution

It establishes a necessary and sufficient condition for rooted trees to have identical plucking polynomials and offers a criterion for realizing integer sequences as rooted trees.

## Key findings

- Two rooted trees have the same plucking polynomial if and only if a specific condition is met.
- A criterion is provided for when a sequence of non-negative integers can be realized as a rooted tree.
- The results deepen the understanding of polynomial invariants in rooted trees.

## Abstract

In this paper we give a sufficient and necessary condition for two rooted trees with the same plucking polynomial. Furthermore, we give a criteria for a sequence of non-negative integers to be realized as a rooted tree.