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Paper   IPM / M / 13616
School of Mathematics
  Title:   On a family of diamond-free strongly regular graphs
1.  A. Mohammadian
2.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: SIAM J. Discrete Math.
  Vol.:  28
  Year:  2014
  Pages:   1906-1915
  Supported by:  IPM
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.

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