---
tag: 0GYQK9NDJF
kind: concept
name: Cayley graph
msc: [05C25, 20F65]
sources:
  - url: https://en.wikipedia.org/wiki/Cayley_graph
    locator: lead section
same_as:
  wikidata: Q859174
  wikipedia: Cayley graph
---

## Summary

The Cayley graph of a group $G$ with a generating set $S$ has the elements of $G$ as vertices. It has an edge from $g$ to $g s$ for each $g \in G$ and $s \in S$.
It encodes the structure of the group as a graph.