{"paper":{"title":"On $2$-arc-transitive graphs of order $kp^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Eric Swartz, Gabriel Verret, Luke Morgan","submitted_at":"2014-12-24T14:25:55Z","abstract_excerpt":"We show that there exist functions $c$ and $g$ such that, if $k$, $n$ and $d$ are positive integers with $d> g(n)$ and $\\Gamma$ is a $d$-valent $2$-arc-transitive graph of order $kp^n$ with $p$ a prime, then $p\\leqslant kc(d)$. In other words, there are only finitely many $d$-valent 2-arc-transitive graphs of order $kp^n$ with $d>g(n)$ and $p$ prime. This generalises a recent result of Conder, Li and Poto\\v{c}nik."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7669","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"}