On a Family of Diamond-Free Strongly Regular Graphs

Abstract

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) + s 2 t(t + 1)/μ, s(t + 1), s − 1, μ). Let S be a PQ(3, (n + 3)(n 2 − 1)/3, n 2 + n) such that for every two noncollinear points p 1 and p 2 , there is a point q noncollinear with p 1 , p 2 , and all points collinear with both p 1 and p 2 . In this article, we establish that S exists only for n ∈ {−2, 2, 3} and probably n = 10.