{"paper":{"title":"There does not exist a distance-regular graph with intersection array $\\{80, 54,12; 1, 6, 60\\}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack H. Koolen, Jongyook Park, Masood Ur Rehman, Quaid Iqbal","submitted_at":"2018-09-26T14:37:49Z","abstract_excerpt":"In this paper we will show that there does not exist a distance-regular graph $\\Gamma$ with intersection array $\\{80, 54,12; 1, 6, 60\\}$. We first show that a local graph $\\Delta$ of $\\Gamma$ does not contain a coclique with 5 vertices, and then we prove that the graph $\\Gamma$ is geometric by showing that $\\Delta$ consists of 4 disjoint cliques with 20 vertices. Then we apply a result of Koolen and Bang to the graph $\\Gamma$, and we could obtain that there is no such a distance-regular graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10029","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"}