Some properties and applications of Hermitian varieties in a finite projective space PG( N, q2) in the construction of strongly regular graphs (two-class association schemes) and block designs

Abstract

The section of a non-degenerate Hermitian variety V N−1 by a polar hyperplane in PG( N, q 2) and the number of u-flats, 0 ≤ u ≤ [ (N − 1) 2 ] , contained in a V N−1 are derived. From the incidence of external points, tangent lines and secant lines with respect to non-degenerate Hermitian varieties in PG(2, q 2) and PG(3, q 2) and the incidence of generators and tangent planes of a nondegenerate Hermitian variety in PG(3, q 2), three different families of strongly regular graphs (two-class association schemes) and block designs are derived.