On quantum symmetries of graphs

Let $G$ be a simple finite graph, and let ${\mathcal{U}}_G$ be the related quantum graph. We study the game algebra $C(\mathrm{Q}\mathrm{u}\mathrm{t}({\mathcal{U}}_G))$ of quantum automorphism of ${\mathcal{U}}_G$. Moreover, we prove that for any graph $G$ with $\mathrm{\mid }V(G)\mathrm{\mid }\ge 3$, the quantum graph ${\mathcal{U}}_G$ admits nonlocal symmetry, meaning that there exists a perfect quantum no-signaling correlation