  In this article we generalize a theorem of Benson for generalized quadrangles
to strongly regular graphs and directed strongly regular graphs. The main
result provides numerical restrictions on the number of fixed vertices and the
number of vertices mapped to adjacent vertices under an automorphism. It is
explained how these results can be used when studying partial difference sets
in Abelian groups and projective two-weight sets. The underlying ideas are
linear algebraic in nature.
