Study of quantum symmetries for vertex-transitive graphs using intertwiner spaces

We study quantum automorphism group of vertex-transitive graphs using intertwinner spaces of the magic unitary matrix associated to this quantum subgroups of $S_n^{+}$. We also give some applications to quantum symmetries of circulant graphs as $C_{13}(3,4)$ and $C_{17}(2,4,8)$.