Graphs cospectral with NU(n + 1,q2), n ≠ 3

Abstract

Let H(n,q2) be a non–degenerate Hermitian variety of PG(n,q2), n≥2. Let NU(n+1,q2) be the graph whose vertices are the points of PG(n,q2)∖H(n,q2) and two vertices P1,P2 are adjacent if the line joining P1 and P2 is tangent to H(n,q2). Then NU(n+1,q2) is a strongly regular graph. In this paper we show that NU(n+1,q2), n≠3, is not determined by its spectrum.