{"paper":{"title":"On solid density of Cayley digraphs on finite Abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. Aguil\\'o, M. Zaragoz\\'a","submitted_at":"2018-06-11T10:51:30Z","abstract_excerpt":"Let $\\Gamma=$Cay$(G,T)$ be a Cayley digraph over a finite Abelian group $G$ with respect the generating set $T\\not\\ni0$. $\\Gamma$ has order ord$(\\Gamma)=|G|=n$ and degree deg$(\\Gamma)=|T|=d$. Let $k(\\Gamma)$ be the diameter of $\\Gamma$ and denote $\\kappa(d,n)=\\min\\{k(\\Gamma):~\\textrm{ord}(\\Gamma)=n,\\textrm{deg}(\\Gamma)=d\\}$.\n  We give a closed expression, $\\ell(d,n)$, of a tight lower bound of $\\kappa(d,n)$ by using the so called {\\em solid density} introduced by Fiduccia, Forcade and Zito.\n  A digraph $\\Gamma$ of degree $d$ is called {\\em tight} when $k(\\Gamma)=\\kappa(d,|\\Gamma|)=\\ell(d,|\\Gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03899","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"}