On a Family of Diamond-Free Strongly Regular Graphs

The existence of a partial quadrangle PQ(s, t, μ) is equivalent to the existence of a diamond-free strongly regular graph SRG(1+s(t+1)+s2t(t+1)/μ, s(t+1), s−1, μ). Let S be a PQ(3, (n + 3)(n2 − 1)/3, n2 + n) such that for every two non-collinear points p1 and p2, there is a point q non-collinear with p1, p2, and all points collinear with both p1 and p2. In this article, we establish that S exists only for n ∈ {−2, 2, 3} and probably n = 10.