{"paper":{"title":"Finite $s$-geodesic transitive graphs under certain girths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun-Jie Huang","submitted_at":"2025-06-06T07:00:34Z","abstract_excerpt":"For an integer $s\\geq1$ and a graph $\\Gamma$, a path $(u_0, u_1, \\ldots, u_{s})$ of vertices of $\\Gamma$ is called an {\\em $s$-geodesic} if it is a shortest path from $u_0$ to $u_{s}$. We say that $\\Gamma$ is {\\em $s$-geodesic transitive} if, for each $i\\leq s$, $\\Gamma$ has at least one $i$-geodesic, and its automorphism group is transitive on the set of $i$-geodesics. In 2021, Jin and Praeger [J. Combin. Theory Ser. A 178 (2021) 105349] have studied $3$-geodesic transitive graphs of girth $5$ or $6$, and they also proposed to the problem that to classify $s$-geodesic transitive graphs of gir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05803","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05803/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}