{"paper":{"title":"A Generalization of Brown's Construction for the Degree/Diameter Problem","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yawara Ishida","submitted_at":"2015-12-30T15:01:18Z","abstract_excerpt":"The degree/diameter problem is the problem of finding the largest possible number of vertices $n_{\\Delta,D}$ in a graph of given degree $\\Delta$ and diameter $D$. We consider the problem for the case of diameter $D=2$. William G Brown gave a lower bound of the order of $(\\Delta,2)$-graph. In this paper, we give a generalization of his construction and improve the lower bounds for the case of $\\Delta=306$ and $\\Delta=307$. One is $(306,2)$-graph with $88723$ vertices, the other is $(307,2)$-graph with $88724$ vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08961","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"}