{"paper":{"title":"Symmetry properties of subdivision graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Alice Devillers, Ashraf Daneshkhah, Cheryl E. Praeger","submitted_at":"2010-08-13T07:42:02Z","abstract_excerpt":"The subdivision graph $S(\\Sigma)$ of a graph $\\Sigma$ is obtained from $\\Sigma$ by `adding a vertex' in the middle of every edge of $\\Si$. Various symmetry properties of $\\S(\\Sigma)$ are studied. We prove that, for a connected graph $\\Sigma$, $S(\\Sigma)$ is locally $s$-arc transitive if and only if $\\Sigma$ is $\\lceil\\frac{s+1}{2}\\rceil$-arc transitive. The diameter of $S(\\Sigma)$ is $2d+\\delta$, where $\\Sigma$ has diameter $d$ and $0\\leqslant \\delta\\leqslant 2$, and local $s$-distance transitivity of $\\S(\\Sigma)$ is defined for $1\\leqslant s\\leqslant 2d+\\delta$. In the general case where $s\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2261","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"}