Quantum automorphism groups of vertex-transitive graphs of order leq 11

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups ${\mathbb Z}_n$, symmetric groups $S_n$ and quantum symmetric groups $\mathcal Q_n$, by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.