{"paper":{"title":"On a family of diamond-free strongly regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Mohammadian, B. Tayfeh-Rezaie","submitted_at":"2013-03-03T07:57:58Z","abstract_excerpt":"The existence of a partial quadrangle ${\\mathsf{PQ}}(s, t, \\mu)$ is equivalent to the existence of a diamond-free strongly regular graph ${\\mathsf{SRG}}(1+s(t+1)+s^2t(t+1)/\\mu, s(t+1), s-1, \\mu)$. Recently, it is shown that there exists a ${\\mathsf{PQ}}(2, (n^3+3n^2-2)/2, n^2+n)$ if and only if $n\\in\\{1, 2, 4\\}$. Let $\\mathcal{S}$ be a ${\\mathsf{PQ}}(3,(n+3)(n^2-1)/3, n^2+n)$ such that for every two non-collinear points $p_1$ and $p_2$, there is a point $q$ non-collinear with $p_1$, $p_2$, and all points collinear with both $p_1$ and $p_2$. In this article, we establish that $\\mathcal{S}$ exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0473","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}