A note on strongly regular graphs and (k,tau)-regular sets

A subset of the vertex set of a graph G, S ⊆ V (G), is a (k, τ)-regular set if it induces a k-regular subgraph of G and every vertex not in the subset has τ neighbors in it. This paper is a contribution to the given problem of existence of (k, τ)-regular sets associated with all distinct eigenvalues of integral strongly regular graphs. The minimal idempotents of the Bose-Mesner algebra of strongly regular graphs are used to obtain a necessary and sufficient condition on the existence of (k, τ)-regular sets for its two restricted eigenvalues.