---
tag: QCZ3NE42AC
kind: concept
name: Distance-transitive graph
aliases: [distance-transitive-graphs]
sources:
  - wikipedia: en:7768222@r1352720983
    locator: Distance-transitive graph
    note: adopted
    mention: wikipedia://en/7768222
    sections: [Summary]
same_as:
  wikidata: Q4391306
  wikipedia: Distance-transitive graph
inventory: [CTCQ3GDJQE]
---

## Summary

In the mathematical field of graph theory, a **distance-transitive graph** is a [[graph|00C0BR7D7H]] such that, given any two vertices $v$ and $w$ at any [[distance|0QV9VNNB4Z]] $i$, and any other two vertices $x$ and $y$ at the same distance, there is an automorphism of the graph that carries $v$ to $x$ and $w$ to $y$. Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and D. H. Smith.