ON A FAMILY OF DIAMOND-FREE STRONGLY REGULAR GRAPHS

The existence of a partial quadrangle PQ(s, t, mu) is equivalent to the existence of a diamond-free strongly regular graph SRG(1 + s(t + 1) + s(2)t(t + 1)/mu, s(t + 1), s - 1, mu). Let S be a PQ(3, (n + 3)(n(2) - 1)/3, n(2) + n) such that for every two noncollinear points p1 and p2, there is a point q noncollinear with p1, p2, and all points collinear with both p1 and p2. In this article, we establish that S exists only for n is an element of {-2, 2, 3} and probably n = 10.