Edge-transitive graph

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]

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

^ Biggs, Norman (1993). Algebraic Graph Theory (2nd ed.). Cambridge: Cambridge University Press. p. 118. ISBN 0-521-45897-8.

[biggs-1] Biggs, Norman (1993). Algebraic Graph Theory (2nd ed.). Cambridge: Cambridge University Press. p. 118. ISBN 0-521-45897-8.

[1]

Graph families defined by their automorphisms
distance-transitive	→	distance-regular	←	strongly regular
↓
symmetric (arc-transitive)	←	t-transitive, $t \geq 2$		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

Edge-transitive graph

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