{"paper":{"title":"A Family of Dense Mixed Graphs of Diameter $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Camino Balbuena, Gabriela Araujo-Pardo, M. Miller, M. \\v{Z}d\\'imalov\\'a","submitted_at":"2015-11-19T03:10:46Z","abstract_excerpt":"A mixed graph is said to be dense if its order is close to the Moore bound and it is optimal if there is not a mixed graph with the same parameters and bigger order.\n  We present a construction that provides dense mixed graphs of undirected degree $q$, directed degree $\\frac{q-1}{2}$ and order $2q^2$, for $q$ being an odd prime power. Since the Moore bound for a mixed graph with these parameters is equal to $\\frac{9q^2-4q+3}{4}$ the defect of these mixed graphs is $({\\frac{q-2}{2}})^2-\\frac{1}{4}$.\n  In particular we obtain a known mixed Moore graph of order $18$, undirected degree $3$ and dir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06050","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"}