# 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.

## Source of Name

This entry was named for Heinz Prüfer.