# Edge-transitive graph

## Graph where all pairs of edges are automorphic / From Wikipedia, the free encyclopedia

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Edge-transitive graph?

Summarize this article for a 10 year old

SHOW ALL QUESTIONS

This article is about graph theory. For edge transitivity in geometry, see Edge-transitive.

In the mathematical field of graph theory, an **edge-transitive graph** is a graph G such that, given any two edges *e*_{1} and *e*_{2} of G, there is an automorphism of G that maps *e*_{1} to *e*_{2}.^{[1]}

**Quick Facts**Graph families defined by their automorphisms, → ...

Graph families defined by their automorphisms | ||||
---|---|---|---|---|

distance-transitive | → | distance-regular | ← | strongly regular |

↓ | ||||

symmetric (arc-transitive) | ← | t-transitive, t ≥ 2 |
skew-symmetric | |

↓ | ||||

_{(if connected)}vertex- and edge-transitive |
→ | edge-transitive and regular | → | edge-transitive |

↓ | ↓ | ↓ | ||

vertex-transitive | → | regular | → | _{(if bipartite)}biregular |

↑ | ||||

Cayley graph | ← | zero-symmetric | asymmetric |

Close

In other words, a graph is edge-transitive if its automorphism group acts transitively on its edges.