Definition:Prüfer Sequence

Definition
A Prüfer sequence of order $n$ is a (finite) sequence of integers:
 * $\left({\mathbf a_1, \mathbf a_2, \ldots, \mathbf a_{n-2}}\right)$

such that $\forall i: 1 \le i \le n-2: 1 \le \mathbf a_i \le n$.

That is, it is a (finite) sequence of $n - 2$ integers between $1$ and $n$.

Also known as
A Prüfer sequence is also known as a Prüfer code.

Historical note
The concept was originally defined for the purposes of demonstrating a proof of Cayley's Formula.