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

AbstractThe section of a non-degenerate Hermitian variety VN−1 by a polar hyperplane in PG(N, q2) and the number of u-flats, 0 ≤ u ≤ [(N − 1)2], contained in a VN−1 are derived. From the incidence of external points, tangent lines and secant lines with respect to non-degenerate Hermitian varieties in PG(2, q2) and PG(3, q2) and the incidence of generators and tangent planes of a nondegenerate Hermitian variety in PG(3, q2), three different families of strongly regular graphs (two-class association schemes) and block designs are derived