A new family of partial geometries (Q1275288)

The point graph of a partial geometry is strongly regular, and a strongly regular graph is called pseudo-geometric if it has the same parameters as the point graph of some partial geometry. The hermitian graph \({\mathcal H}(q)\) is known to be pseudo-geometric, but in general it is not geometric, i.e. it does not arise as the point graph of a partial geometry. The author proves that for \(q = 3^{2n}\) the hermitian graph actually is geometric. The automorphism group of the corresponding partial geometry is a subgroup of index 4 in the automorphism group of \({\mathcal H}(3^{2n})\).