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We show that $\\gamma(P_f(n,2))=\\gamma(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $\\gamma(P_f(n,2))=\\gamma(P(n,2))$ for the other cases."},"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":"1305.1366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T00:47:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cd77d48adb558e4c17d9c0e70bd737f82088dff2d199126f0cdd6173251123a4","abstract_canon_sha256":"648ac38ae83519f13c12b2edbeb2ea655ebb581bab14677a2e36bd6d6da3ca3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:19.506060Z","signature_b64":"y1InYEloJaD9SBbDoun7tyAexNgjXWOAk8BoNgNykvl6t9f8G1ceoHQrWbX/8IVHjZJ1c79mSXPn85IZJZAOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8c11fa2ab6a80db0388a30168891599decff2193fd6271455904be111a6dda7","last_reissued_at":"2026-05-18T03:14:19.504781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:19.504781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Domination Number of Generalized Petersen Graphs with a Faulty Vertex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Jun-Lin Guo, Kuo-Hua Wu, Ton Kloks, Yue-Li Wang","submitted_at":"2013-05-07T00:47:55Z","abstract_excerpt":"In this paper, we investigate the domination number of generalized Petersen graphs P(n, 2) when there is a faulty vertex. Denote by $\\gamma(P(n,2))$ the domination number of P(n,2) and $\\gamma(P_f(n,2))$ the domination number of P(n,2) with a faulty vertex $u_f$. We show that $\\gamma(P_f(n,2))=\\gamma(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $\\gamma(P_f(n,2))=\\gamma(P(n,2))$ for the other cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1366","kind":"arxiv","version":2},"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":"1305.1366","created_at":"2026-05-18T03:14:19.504884+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.1366v2","created_at":"2026-05-18T03:14:19.504884+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1366","created_at":"2026-05-18T03:14:19.504884+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDAR7IVLNKAN","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDAR7IVLNKANWA4I","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDAR7IVL","created_at":"2026-05-18T12:28:09.283467+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/ZDAR7IVLNKANWA4IUMAWRCIVTH","json":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH.json","graph_json":"https://pith.science/api/pith-number/ZDAR7IVLNKANWA4IUMAWRCIVTH/graph.json","events_json":"https://pith.science/api/pith-number/ZDAR7IVLNKANWA4IUMAWRCIVTH/events.json","paper":"https://pith.science/paper/ZDAR7IVL"},"agent_actions":{"view_html":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH","download_json":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH.json","view_paper":"https://pith.science/paper/ZDAR7IVL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.1366&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDAR7IVLNKANWA4IUMAWRCIVTH/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDAR7IVLNKANWA4IUMAWRCIVTH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/action/storage_attestation","attest_author":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/action/author_attestation","sign_citation":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/action/citation_signature","submit_replication":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/action/replication_record"}},"created_at":"2026-05-18T03:14:19.504884+00:00","updated_at":"2026-05-18T03:14:19.504884+00:00"}