{"paper":{"title":"Domination ratio of integer distance digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jia Huang","submitted_at":"2019-03-05T14:28:04Z","abstract_excerpt":"An integer distance digraph is the Cayley graph $\\Gamma(\\mathbb{Z},S)$ of the additive group $\\mathbb{Z}$ of all integers with respect to some finite subset $S \\subseteq \\mathbb{Z}$. The domination ratio of $\\Gamma(\\mathbb{Z},S)$ is the minimum density of a dominating set in $\\Gamma(\\mathbb{Z},S)$. We establish some basic results on the domination ratio of $\\Gamma(\\mathbb{Z},S)$ and precisely determine it when $S=\\{s,t\\}$ with $s$ dividing $t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01844","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"}