{"paper":{"title":"The uniqueness of a distance-regular graph with intersection array {32,27,8,1;1,4,27,32} and related results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Leonard H. Soicher","submitted_at":"2015-12-18T14:44:43Z","abstract_excerpt":"It is known that, up to isomorphism, there is a unique distance-regular graph $\\Delta$ with intersection array {32,27;1,12} (equivalently, $\\Delta$ is the unique strongly regular graph with parameters (105,32,4,12)). Here we investigate the distance-regular antipodal covers of $\\Delta$. We show that, up to isomorphism, there is just one distance-regular antipodal triple cover of $\\Delta$ (a graph $\\hat\\Delta$ discovered by the author over twenty years ago), proving that there is a unique distance-regular graph with intersection array {32,27,8,1;1,4,27,32}. In the process, we confirm an unpubli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05976","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"}