---
tag: ZBFQ8EB1RV
kind: concept
name: Recursive tree
aliases: [recursive-trees]
sources:
  - wikipedia: en:5140949@r1285922157
    locator: Recursive tree
    note: adopted
    mention: wikipedia://en/5140949
    sections: [Summary]
same_as:
  wikidata: Q17133279
  wikipedia: Recursive tree
inventory: [44H7SKMKSN]
---

## Summary

In graph theory, a **recursive tree** (i.e., unordered tree) is a labeled, rooted [[tree|062D9KXJB1]]. A size-$n$ recursive tree's vertices are labeled by distinct positive integers $1, 2, \ldots, n$, where the labels are strictly increasing starting at the root labeled 1. Recursive trees are [[non-planar|029JQEK15B]], which means that the children of a particular vertex are not ordered; for example, the following two size-3 recursive trees are equivalent: ${}_{3}/^{1}\backslash_{2} =_{2}/^{1}\backslash_{3}$.