Partitioning strongly regular graphs (Q1062989)

An interesting investigation of strongly regular graphs whose vertices can be partitioned into two subsets of equal size on each of which a strongly regular subgraph is induced. Examples are the Higman-Sims graph, the subconstituents of the McLaughlin graph, and some graphs constructed from difference sets. In general, such graphs must belong either to the two parameter family of Smith graphs, or to a special one parameter family of graphs.