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The generalized Sierpi\\'{n}ski triangle graph $\\hat{S_p^n}$ is obtained by contracting all non-clique edges from the Sierpi\\'{n}ski graph $S_p^{n+1}$. We prove that $\\tau(\\hat{S}_3^n)=\\frac {3^n+1} 2=\\frac{|V(\\hat{S}_3^n)|} 3$, and give an upper bound for $\\tau(\\hat{S}_p^n)$ for the case when $p\\geq 4$."},"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":"1710.01947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-05T10:14:12Z","cross_cats_sorted":[],"title_canon_sha256":"a444c9dc89b8fc3c485495996494e6443d95b4ac1a187b13adcf142c41d389b8","abstract_canon_sha256":"a0a201e3beb568f20bf88c418e1627a6ac6c1b53796596b33b715e5eb263f714"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:38.000281Z","signature_b64":"NL9eoc/bd7ze6Ga3ixHSCIDq7acxnwnI2yms9Y96rWjBhUuHMH0wL0I4mg33XVjRHTlTN3ExYxdFdYTozHYXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78b25623ddb463311b8783b2166ae27c52c3a4675385e576547fb932354e1527","last_reissued_at":"2026-05-18T00:33:37.999789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:37.999789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Feedback vertex number of Sierpi\\'{n}ski-type graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Baoyindureng Wu, Biao Zhao, LiLi Yuan","submitted_at":"2017-10-05T10:14:12Z","abstract_excerpt":"The feedback vertex number $\\tau(G)$ of a graph $G$ is the minimum number of vertices that can be deleted from $G$ such that the resultant graph does not contain a cycle. 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We prove that $\\tau(\\hat{S}_3^n)=\\frac {3^n+1} 2=\\frac{|V(\\hat{S}_3^n)|} 3$, and give an upper bound for $\\tau(\\hat{S}_p^n)$ for the case when $p\\geq 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01947","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":"1710.01947","created_at":"2026-05-18T00:33:37.999864+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.01947v1","created_at":"2026-05-18T00:33:37.999864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01947","created_at":"2026-05-18T00:33:37.999864+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCZFMI65WRRT","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCZFMI65WRRTCG4H","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCZFMI65","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/PCZFMI65WRRTCG4HQOZBM2XCPR","json":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR.json","graph_json":"https://pith.science/api/pith-number/PCZFMI65WRRTCG4HQOZBM2XCPR/graph.json","events_json":"https://pith.science/api/pith-number/PCZFMI65WRRTCG4HQOZBM2XCPR/events.json","paper":"https://pith.science/paper/PCZFMI65"},"agent_actions":{"view_html":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR","download_json":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR.json","view_paper":"https://pith.science/paper/PCZFMI65","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.01947&json=true","fetch_graph":"https://pith.science/api/pith-number/PCZFMI65WRRTCG4HQOZBM2XCPR/graph.json","fetch_events":"https://pith.science/api/pith-number/PCZFMI65WRRTCG4HQOZBM2XCPR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR/action/storage_attestation","attest_author":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR/action/author_attestation","sign_citation":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR/action/citation_signature","submit_replication":"https://pith.science/pith/PCZFMI65WRRTCG4HQOZBM2XCPR/action/replication_record"}},"created_at":"2026-05-18T00:33:37.999864+00:00","updated_at":"2026-05-18T00:33:37.999864+00:00"}