{"paper":{"title":"Switched symplectic graphs and their 2-ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aida Abiad, Willem H. Haemers","submitted_at":"2014-12-09T12:55:15Z","abstract_excerpt":"We apply Godsil-McKay switching to the symplectic graphs over $\\mathbb{F}_2$ with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new strongly regular graph with parameters $(2^{2\\nu}\\!-1, 2^{2\\nu-1}, 2^{2\\nu-2},2^{2\\nu-2})$ and 2-rank $2\\nu+2$ when $\\nu\\geq 3$. For the symplectic graph on $63$ vertices we investigate repeated switching by computer and find many new strongly regular graphs with the above parameters for $\\nu=3$ with various 2-ranks. Using these results and a recursive constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2945","kind":"arxiv","version":2},"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"}