{"paper":{"title":"On graphs of defect at most 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guillermo Pineda-Villavicencio, Mirka Miller, Ramiro Feria-Pur\\'on","submitted_at":"2010-10-27T11:55:22Z","abstract_excerpt":"In this paper we consider the degree/diameter problem, namely, given natural numbers {\\Delta} \\geq 2 and D \\geq 1, find the maximum number N({\\Delta},D) of vertices in a graph of maximum degree {\\Delta} and diameter D. In this context, the Moore bound M({\\Delta},D) represents an upper bound for N({\\Delta},D). Graphs of maximum degree {\\Delta}, diameter D and order M({\\Delta},D), called Moore graphs, turned out to be very rare. Therefore, it is very interesting to investigate graphs of maximum degree {\\Delta} \\geq 2, diameter D \\geq 1 and order M({\\Delta},D) - {\\epsilon} with small {\\epsilon} >"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5658","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"}