  In this paper, we show that if G is strongly regular then the Gallai graph
and the anti-Gallai graph of G are edge-regular. We also identify conditions
under which the Gallai and anti-Gallai graphs are themselves strongly regular,
as well as conditions under which they are 2-connected. We include also a
number of concrete examples and a discussion of spectral properties of the
Gallai and anti-Gallai graphs.
