---
tag: 0GDQRETR59
kind: concept
name: Prüfer sequence
msc: [05C05]
sources:
  - url: https://en.wikipedia.org/wiki/Prüfer_sequence
    locator: Algorithm to convert a  tree into a Prüfer sequence
same_as:
  wikidata: Q1087829
  wikipedia: Prüfer sequence
---

## Summary

The Prüfer sequence encodes a labelled tree on $n$ vertices as a sequence of $n - 2$ labels. This encoding is a bijection, and it proves Cayley's formula. The node [[Prüfer sequence|09PV9JSY6E]] gives the precise definition.