Intriguing Sets of Points of Q(2n, 2) \Q +(2n - 1, 2)

Intriguing sets of vertices have been studied for several classes of strongly regular graphs. In the present paper, we study intriguing sets for the graphs Γn, n ≥ 2, which are defined as follows. Suppose Q(2n, 2), n ≥ 2, is a nonsingular parabolic quadric of PG(2n, 2) and Q+(2n − 1, 2) is a nonsingular hyperbolic quadric obtained by intersecting Q(2n, 2) with a suitable nontangent hyperplane. Then the collinearity relation of Q(2n, 2) defines a strongly regular graph Γn on the set Q(2n, 2) \Q+(2n− 1, 2). We describe some classes of intriguing sets of Γn and classify all intriguing sets of Γ2 and Γ3.