New strongly regular graphs from finite geometries via switching

We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type U(n,2), O(n,3), O(n,5), O⁺(n,3), and O⁻(n,3) are not determined by its parameters for n≥6. We prove this by using a variation of Godsil-McKay switching recently described by Wang, Qiu, and Hu. This also results in a new, shorter proof of a previous result of the first author which showed that the collinearity graph of a polar space is not determined by its spectrum. The same switching gives a linear algebra explanation for the construction of a large number of non-isomorphic designs.