{"paper":{"title":"Finite 2-distance transitive graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Brian P. Corr, Csaba Schneider, Wei Jin","submitted_at":"2015-07-03T20:55:41Z","abstract_excerpt":"A non-complete graph $\\Gamma$ is said to be $(G,2)$-distance transitive if $G$ is a subgroup of the automorphism group of $\\Gamma$ that is transitive on the vertex set of $\\Gamma$, and for any vertex $u$ of $\\Gamma$, the stabilizer $G_u$ is transitive on the sets of vertices at distance 1 and 2 from $u$. This paper investigates the family of $(G,2)$-distance transitive graphs that are not $(G,2)$-arc transitive. Our main result is the classification of such graphs of valency not greater than 5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01027","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"}