ON A FAMILY OF DIAMOND-FREE STRONGLY REGULAR GRAPHS

摘要

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~2t(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.