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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.02029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-08T13:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"ca59e55b6a98b7c52e326e056cb5a1cd795fb3af856a1d5122f780ed5be04ef9","abstract_canon_sha256":"b5ef91f35c0a8b2b953b5c3289e09e6874025abf4938757c4b340699e59ffe3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:38.130659Z","signature_b64":"KDpZQsLV5DUfmHmcAV7ykLQJz/PyXX/Tf8uJrT4qoG61wMa6L7FjBpYLVgCeXP/JRIKummnPCB9zmP7oZ7/pBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea529323ae8d6f3cb45dd936d089aa0ff7e251823d804e17453816a35fef2b4b","last_reissued_at":"2026-05-18T02:16:38.130036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:38.130036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $v$. 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