---
tag: 2JMR6X47R0
kind: concept
name: Vertex-transitive graph
sources:
  - wikipedia: en:581175@r1310100542
    locator: Vertex-transitive graph
    note: adopted
    mention: wikipedia://en/581175
    sections: [Summary]
same_as:
  wikidata: Q220997
  wikipedia: Vertex-transitive graph
inventory: [6M2DR8XT7K]
---

## Summary

In the mathematical field of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is a **vertex-transitive graph** if, given any two vertices $v_{1}$ and $v_{2}$ of $G$, there is an automorphism $f$ such that