Edge-transitive graph
From Wikipedia, the free encyclopedia
| Some graph families defined by their automorphisms | ||
| distance-transitive |  |
distance-regular |
 |
||
| symmetric (arc-transitive) | |
edge-transitive |
| (if connected) |
||
| vertex-transitive |  |
Cayley graph |
|
||
| regular | ||
This article is about graph theory. For edge transitivity in geometry, see Edge-transitive.
In mathematics, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism of G that maps e1 to e2.
In other words, a graph is edge-transitive if its automorphism group acts transitively upon its edges.
[edit] Examples and properties
- Any complete bipartite graph Km,n is edge-transitive.
- Any edge-transitive graph that is not vertex-transitive is bipartite. These graphs are called semi-symmetric.
- Any symmetric graph is edge-transitive.
[edit] See also
- Vertex-transitive graph
- Arc-transitive graph
- Edge-transitive (in geometry)
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