On a graph isomorphic to NO+(6,2)

Let Q+(2n − 1, 2) be a non-degenerate hyperbolic quadric of P G(2n − 1, 2). Let NO+(2n, 2) be the tangent graph, whose vertices are the points of P G(2n−1, 2)\Q+(2n−1, 2) and two vertices u, v are adjacent if the line joining u and v is tangent to Q+(2n−1, 2). Then NO+(2n−1, q) is a strongly regular graph. Let V 4 2 be the Veronese surface in P G(5, q), and M3 4 its secant variety. When q = 2, |Q+(5, 2)| = |M3 4 | = 35. In this paper we define the graph NM3 4 , with 28 vertices in P G(5, 2) \M3 4 and with the analogue incidence rule of the tangent graph. Such graph is isomorphic to NO+(6, 2).