Hello,

I have the following proof of Cayley's Theorem: Proof.

This proof counts orderings of directed edges of rooted trees in two ways and concludes the number of rooted trees with directed edges of order $n$.

However, I know a version of Cayley's Theorem in which $n^{n-2}$ is the number of marked trees spanning $K_{n}$.

What I need is to show that the number of marked trees spanning $K_{n}$ is equal to the number of rooted trees with directed edges of order $n$. This way, the proof given above will be valid for the version I know of the theorem.

As I understand, rooted trees and rooted trees with directed edges are the same thing. It shouldn't be hard to prove anyway. The rest, I don't know.

Thanks.