---
tag: R53ANW6ZTK
kind: concept
name: Uniform tree
sources:
  - wikipedia: en:19146037@r1317749502
    locator: Uniform tree
    note: adopted
    mention: wikipedia://en/19146037
    sections: [Summary]
same_as:
  wikidata: Q7885123
  wikipedia: Uniform tree
inventory: [7ASE2SNWG2]
---

## Summary

In mathematics, a **uniform tree** is a locally finite [[tree|062D9KXJB1]] which is the universal cover of a finite graph. Equivalently, the full [[automorphism group|0CWXCWP0Y0]] $G=Aut(X)$ of the tree, which is a locally compact topological group, is unimodular and $G/X$ is finite. Also equivalent is the existence of a uniform X-lattice in $G$.