AbstractWe investigate strongly regular graphs for which Hoffman's ratio bound and Cvetcović's inertia bound are equal. This means that, wherevis the number of vertices,kis the regularity,is the smallest eigenvalue, andis the multiplicity of. We show that Delsarte cocliques do not exist for all Taylor's 2‐graphs and for point graphs of generalized quadrangles of orderfor infinitely manyq. For cases where equality may hold, we show that for nearly all parameter sets, there are at most two Delsarte cocliques.