A spectral proof of the uniqueness of a strongly regular graph with parameters (81,20,1,6)(81,20,1,6)

We give a new proof that there exists a unique strongly regular graph with parameters (81,20,1,6)(81,20,1,6). Unlike the finite geometry approach used by Brouwer and Haemers, we use linear algebra and spectral graph theory concepts, namely the technique of star complements, in our proof.