Hello,


I have the following proof of Cayley's Theorem: [Proof](http://imageshack.us/photo/my-images/821/sformulaproof.png).


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.



Cayley's Theorem regarding marked trees
What is the question? This proof is in "Proofs from the Book" and credited to Jim Pitman.


