Definition:Prüfer Sequence

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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.