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Arc transitivity of the complete graph
Recall that a graph $G$ is arc transitive if the natural action of $\mathrm{Aut}(G)$ on $A(G) = \{ (u,v) | \{u,v\} \in E(G)\}$ is transitive.
In other words, given $(u,v),(u'.v') \in A(G)$ one finds ...
