Quantum automorphism groups of vertex-transitive graphs of order $\le 11$

Abstract

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.

20 pages, final version