A telescopic proof of Cayley's formula

TL;DR

This paper presents a concise, novel proof demonstrating that the number of labeled trees on n vertices is n^{n-2}, offering a new perspective on Cayley's formula.

Contribution

It introduces a new telescopic proof method for Cayley's formula, differing from existing proofs.

Findings

Confirmed the validity of the telescopic proof approach

Reinforced the count of labeled trees as n^{n-2}

Provided an alternative proof technique for Cayley's formula

Abstract

We give a short proof of the fact that the number of labelled trees on $n$ vertices is $n^{n-2}$. Although many short proofs are known, we have not seen this one before.