{"paper":{"title":"On diregular digraphs with degree two and excess two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"James Tuite","submitted_at":"2017-04-28T21:05:11Z","abstract_excerpt":"An important topic in the design of efficient networks is the construction of $(d,k,+\\epsilon )$-digraphs, i.e. $k$-geodetic digraphs with minimum out-degree $\\geq d$ and order $M(d,k)+ \\epsilon $, where $M(d,k)$ represents the Moore bound for degree $d$ and diameter $k$ and $\\epsilon > 0$ is the (small) excess of the digraph. Previous work has shown that there are no $(2,k,+1)$-digraphs for $k \\geq 2$. In a separate paper, the present author has shown that any $(2,k,+2)$-digraph must be diregular for $k \\geq 2$. In the present work, this analysis is completed by proving the nonexistence of di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00075","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"}