{"paper":{"title":"Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack E. Graver, Mark E. Watkins","submitted_at":"2018-11-29T23:01:31Z","abstract_excerpt":"We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph $\\Lambda$ and a \"code\" assigned to each orbit of Aut($\\Lambda$), there exists a unique lobe-transitive graph $\\Gamma$ of connectivity 1 whose lobes are copies of $\\Lambda$ and is consistent with the given code at every vertex of $\\Gamma$. These results lead to necessary and sufficient conditions for a graph of connectivity $1$ to be edge-transitive and to be arc-transitive. Countable graphs of connectivit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12528","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"}