{"paper":{"title":"Asymptotic enumeration of vertex-transitive graphs of fixed valency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gabriel Verret, Pablo Spiga, Primoz Potocnik","submitted_at":"2012-10-21T15:07:35Z","abstract_excerpt":"Let $G$ be a group and let $S$ be an inverse-closed and identity-free generating set of $G$. The \\emph{Cayley graph} $\\Cay(G,S)$ has vertex-set $G$ and two vertices $u$ and $v$ are adjacent if and only if $uv^{-1}\\in S$. Let $CAY_d(n)$ be the number of isomorphism classes of $d$-valent Cayley graphs of order at most $n$. We show that $\\log(CAY_d(n))\\in\\Theta (d(\\log n)^2)$, as $n\\to\\infty$. We also obtain some stronger results in the case $d=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5736","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"}