  The study of graph C*-algebras has a long history in operator algebras.
Surprisingly, their quantum symmetries have never been computed so far. We
close this gap by proving that the quantum automorphism group of a finite,
directed graph without multiple edges acts maximally on the corresponding graph
C*-algebra. This shows that the quantum symmetry of a graph coincides with the
quantum symmetry of the graph C*-algebra. In our result, we use the definition
of quantum automorphism groups of graphs as given by Banica in 2005. Note that
Bichon gave a different definition in 2003; our action is inspired from his
work. We review and compare these two definitions and we give a complete table
of quantum automorphism groups (with respect to either of the two definitions)
for undirected graphs on four vertices.
