{"paper":{"title":"Vertex-transitive graphs and their arc-types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arjana \\v{Z}itnik, Marston Conder, Toma\\v{z} Pisanski","submitted_at":"2015-05-08T13:22:37Z","abstract_excerpt":"Let $X$ be a finite vertex-transitive graph of valency $d$, and let $A$ be the full automorphism group of $X$. Then the arc-type of $X$ is defined in terms of the sizes of the orbits of the action of the stabiliser $A_v$ of a given vertex $v$ on the set of arcs incident with $v$. Specifically, the arc-type is the partition of $d$ as the sum $$n_1 + n_2 + \\dots + n_t + (m_1 + m_1) + (m_2 + m_2) + \\dots + (m_s + m_s),$$ where $n_1, n_2, \\dots, n_t$ are the sizes of the self-paired orbits, and $m_1,m_1, m_2,m_2, \\dots, m_s,m_s$ are the sizes of the non-self-paired orbits, in descending order.\n  I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02029","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"}