I'm looking for graph $G$ such that $G$ is edge-transitive but $G^c$ is not edge-transitive.
My conjecture:If $G$ is edge-transitive then $G^c$ is edge-transitive
Please advise me.
I'm looking for graph $G$ such that $G$ is edge-transitive but $G^c$ is not edge-transitive.
My conjecture:If $G$ is edge-transitive then $G^c$ is edge-transitive
Please advise me.
An easy counterexample - the graph which is edge-transitive and its complement is not: simply take one edge in $K_4$ as you graph. (The complement is $K_4$ with one edge omitted.)
Graph:
Complement:
Complement can be redrawn like this:
Note that the edge joining the vertices of degree 3 cannot be mapped to any other edge.