{"paper":{"title":"Infinite Families of Asymmetric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adam Gregory, Alejandra Brewer, Darren A. Narayan, Quindel Jones, Rigoberto Florez","submitted_at":"2018-11-28T16:24:58Z","abstract_excerpt":"A graph $G$ is \\textit{asymmetric} if its automorphism group of vertices is trivial. Asymmetric graphs were introduced by Erd\\H{o}s and R\\'{e}nyi in 1963. They showed that the probability of a graph on $n$ vertices being asymmetric tends to $1$ as $n$ tends to infinity. In this paper, we first give consider the number of asymmetric trees, a question posed by Erd\\H{o}s and R\\'enyi. We give a partial result, showing that the number of asymmetric subdivided stars is approximately $q(n-1) - \\lfloor \\frac{n-1}{2} \\rfloor$ where $q(n)$ is the number of ways to sum to $n$ using distinct positive inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11655","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"}