The automorphism group of NU(3,q^2)

Abstract

Let H(n, q^2) be a non-degenerate Hermitian variety of PG(n,q^2), n ge 2. Let NU(n+1,q^2) be the graph whose vertices are the points of PG(n,q^2) setminus H(n,q^2) and two vertices u, v are adjacent if the line joining u and v is tangent to H(n, q^2 ). Then NU(n + 1, q^2) is a strongly regular graph. In this paper we show that the automorphism group of the graph NU(3,q^2) is isomorphic either to PGamma U(3,q), the automorphism group of the projective unitary group PGU(3, q), or to S_{3} wr S_4, according as q ne 2, or q=2.