# Example of Edge-transitive

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

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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.)