The Gallai and Anti-Gallai Graphs of Strongly Regular Graphs

In this paper, we show that if G is strongly regular then the Gallai graph Gamma(G) and the anti-Gallai graph Delta(G) 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.