{"paper":{"title":"Maximizing the order of a regular graph of given valency and second eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Hiroshi Nozaki, Jack H. Koolen, Jason R. Vermette, Sebastian M. Cioab\\u{a}","submitted_at":"2015-03-21T11:13:58Z","abstract_excerpt":"From Alon and Boppana, and Serre, we know that for any given integer $k\\geq 3$ and real number $\\lambda<2\\sqrt{k-1}$, there are finitely many $k$-regular graphs whose second largest eigenvalue is at most $\\lambda$. In this paper, we investigate the largest number of vertices of such graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06286","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"}