{"paper":{"title":"Locally triangular graphs and rectagraphs with symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Alice Devillers, Cheryl E. Praeger, Joanna B. Fawcett, John Bamberg","submitted_at":"2014-07-31T08:37:39Z","abstract_excerpt":"Locally triangular graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every $2$-arc lies in a unique quadrangle. A graph $\\Gamma$ is locally rank 3 if there exists $G\\leq \\mathrm{Aut}(\\Gamma)$ such that for each vertex $u$, the permutation group induced by the vertex stabiliser $G_u$ on the neighbourhood $\\Gamma(u)$ is transitive of rank 3. One natural place to seek locally rank 3 graphs is among the locally triangular graphs, where every induced neighbourhood graph is isomorphic to a triangular graph $T_n$. This is because the grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8312","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"}