Strongly Regular Graph and GI-Completeness It is not known if graph isomorphism (GI) for strongly regular graphs (SRGs) is in P. Are there any hints that it might or might not be GI-Complete? Are there any strong consequences in such cases? (Similar to the belief that GI may not be NP-Complete).
I believe all known GI-completeness results are functorial (definition in the paper), and Babai has recently shown (ITCS 2014, free author's copy) - based on bounds on the structure of automorphism groups of strongly regular graphs - that there is no functorial reduction from GI to strongly regular GI.