A note on 2-local automorphisms of digraph algebras

In this note we show that every 2-local automorphism of a digraph algebra is an automorphism if in addition is symmetric. Moreover, we produce an example to clarify that the conclusion may not be true if has not the extra condition of symmetry. By this means, we give a negative answer to the question about whether every 2-local automorphism of a digraph algebra is automatically an automorphism.