{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PBAHLO3RH6SIBZK456QDU22LYR","short_pith_number":"pith:PBAHLO3R","schema_version":"1.0","canonical_sha256":"784075bb713fa480e55cefa03a6b4bc44a0e0b8b93983f80287c5714b8901a94","source":{"kind":"arxiv","id":"1707.04969","version":1},"attestation_state":"computed","paper":{"title":"On basic graphs of symmetric graphs of valency five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Da-Wei Yang, Jaeun Lee, Jin Ho Kwak, Yan-Quan Feng","submitted_at":"2017-07-17T00:50:56Z","abstract_excerpt":"A graph $\\G$ is {\\em symmetric} or {\\em arc-transitive} if its automorphism group $\\Aut(\\G)$ is transitive on the arc set of the graph, and $\\G$ is {\\em basic} if $\\Aut(\\G)$ has no non-trivial normal subgroup $N$ such that the quotient graph $\\G_N$ has the same valency with $\\G$. In this paper, we classify symmetric basic graphs of order $2qp^n$ and valency 5, where $q<p$ are two primes and $n$ is a positive integer. It is shown that such a graph is isomorphic to a family of Cayley graphs on dihedral groups of order $2q$ with $5\\di (q-1)$, the complete graph $K_6$ of order $6$, the complete bi"},"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":"1707.04969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-17T00:50:56Z","cross_cats_sorted":[],"title_canon_sha256":"3e895606470d827217ca2439b5de8efb9ce525fe4e426a8a7481931cbb5ce384","abstract_canon_sha256":"24e75b10a93a684623632517e2832c83f601819bdbaca6caeff7ab424f342388"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:11.691630Z","signature_b64":"P7gr43kF26PJ/V4OCWExZFNGOAxOSEv/Xs8JKbSeRAR1LZrg8ybPBLwClW07GPe/lK5hDUeUeJWrRkJ0lAmhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"784075bb713fa480e55cefa03a6b4bc44a0e0b8b93983f80287c5714b8901a94","last_reissued_at":"2026-05-18T00:40:11.691064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:11.691064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On basic graphs of symmetric graphs of valency five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Da-Wei Yang, Jaeun Lee, Jin Ho Kwak, Yan-Quan Feng","submitted_at":"2017-07-17T00:50:56Z","abstract_excerpt":"A graph $\\G$ is {\\em symmetric} or {\\em arc-transitive} if its automorphism group $\\Aut(\\G)$ is transitive on the arc set of the graph, and $\\G$ is {\\em basic} if $\\Aut(\\G)$ has no non-trivial normal subgroup $N$ such that the quotient graph $\\G_N$ has the same valency with $\\G$. In this paper, we classify symmetric basic graphs of order $2qp^n$ and valency 5, where $q<p$ are two primes and $n$ is a positive integer. It is shown that such a graph is isomorphic to a family of Cayley graphs on dihedral groups of order $2q$ with $5\\di (q-1)$, the complete graph $K_6$ of order $6$, the complete bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04969","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.04969","created_at":"2026-05-18T00:40:11.691157+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04969v1","created_at":"2026-05-18T00:40:11.691157+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04969","created_at":"2026-05-18T00:40:11.691157+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBAHLO3RH6SI","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBAHLO3RH6SIBZK4","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBAHLO3R","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR","json":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR.json","graph_json":"https://pith.science/api/pith-number/PBAHLO3RH6SIBZK456QDU22LYR/graph.json","events_json":"https://pith.science/api/pith-number/PBAHLO3RH6SIBZK456QDU22LYR/events.json","paper":"https://pith.science/paper/PBAHLO3R"},"agent_actions":{"view_html":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR","download_json":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR.json","view_paper":"https://pith.science/paper/PBAHLO3R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04969&json=true","fetch_graph":"https://pith.science/api/pith-number/PBAHLO3RH6SIBZK456QDU22LYR/graph.json","fetch_events":"https://pith.science/api/pith-number/PBAHLO3RH6SIBZK456QDU22LYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR/action/storage_attestation","attest_author":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR/action/author_attestation","sign_citation":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR/action/citation_signature","submit_replication":"https://pith.science/pith/PBAHLO3RH6SIBZK456QDU22LYR/action/replication_record"}},"created_at":"2026-05-18T00:40:11.691157+00:00","updated_at":"2026-05-18T00:40:11.691157+00:00"}