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A spread of strongly regular graphs is a partition of the vertex set by Delsarte cliques. We consider imprimitive association schemes of class four which are two-fold covers of strongly regular graphs with spreads. It will be shown that a two-fold cover of a strongly regular graph with a spread provides a five class fission scheme of the imprimitive scheme of class four.

A two-fold cover of strongly regular graphs with spreads and association schemes of class five