{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7CFXNEPWO3AGUFJMQ6W2HNNYQ3","short_pith_number":"pith:7CFXNEPW","schema_version":"1.0","canonical_sha256":"f88b7691f676c06a152c87ada3b5b886dd36c1a4a2dfa92487806f4a7eb58cc8","source":{"kind":"arxiv","id":"1103.2419","version":1},"attestation_state":"computed","paper":{"title":"Roman domination number of Generalized Petersen Graphs P(n,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunnian Ji, Haoli Wang, Xirong Xu, Yuansheng Yang","submitted_at":"2011-03-12T03:56:44Z","abstract_excerpt":"A $Roman\\ domination\\ function$ on a graph $G=(V, E)$ is a function $f:V(G)\\rightarrow\\{0,1,2\\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The $weight$ of a Roman domination function $f$ is the value $f(V(G))=\\sum_{u\\in V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is called the $Roman\\ domination\\ number$ of $G$, denoted by $\\gamma_{R}(G)$. In this paper, we study the {\\it Roman domination number} of generalized Petersen graphs P(n,2) and prove that $\\gamma_R(P(n,2)) = \\lceil {\\frac{8n}{7}}"},"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":"1103.2419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-12T03:56:44Z","cross_cats_sorted":[],"title_canon_sha256":"a9d57a6618e7e44fd75d67f4ec40589ffdd3d0a6a93227296fa7d547ffcbb00b","abstract_canon_sha256":"32c823c545f319a0bcd06094125a62bed6b49aef19a58eb95408873a215d6d54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:19.797186Z","signature_b64":"OUUZqF9anCJl8looYSrKr2pURQ8wOuM7bwb9SbOiQVa4eSGTeN7EiRqcOIdLKZqxlXkVWNv1fqxe22rB2I3SAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f88b7691f676c06a152c87ada3b5b886dd36c1a4a2dfa92487806f4a7eb58cc8","last_reissued_at":"2026-05-18T02:22:19.796651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:19.796651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Roman domination number of Generalized Petersen Graphs P(n,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunnian Ji, Haoli Wang, Xirong Xu, Yuansheng Yang","submitted_at":"2011-03-12T03:56:44Z","abstract_excerpt":"A $Roman\\ domination\\ function$ on a graph $G=(V, E)$ is a function $f:V(G)\\rightarrow\\{0,1,2\\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The $weight$ of a Roman domination function $f$ is the value $f(V(G))=\\sum_{u\\in V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is called the $Roman\\ domination\\ number$ of $G$, denoted by $\\gamma_{R}(G)$. In this paper, we study the {\\it Roman domination number} of generalized Petersen graphs P(n,2) and prove that $\\gamma_R(P(n,2)) = \\lceil {\\frac{8n}{7}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2419","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":"1103.2419","created_at":"2026-05-18T02:22:19.796732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.2419v1","created_at":"2026-05-18T02:22:19.796732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2419","created_at":"2026-05-18T02:22:19.796732+00:00"},{"alias_kind":"pith_short_12","alias_value":"7CFXNEPWO3AG","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7CFXNEPWO3AGUFJM","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7CFXNEPW","created_at":"2026-05-18T12:26:22.705136+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/7CFXNEPWO3AGUFJMQ6W2HNNYQ3","json":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3.json","graph_json":"https://pith.science/api/pith-number/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/graph.json","events_json":"https://pith.science/api/pith-number/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/events.json","paper":"https://pith.science/paper/7CFXNEPW"},"agent_actions":{"view_html":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3","download_json":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3.json","view_paper":"https://pith.science/paper/7CFXNEPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.2419&json=true","fetch_graph":"https://pith.science/api/pith-number/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/action/storage_attestation","attest_author":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/action/author_attestation","sign_citation":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/action/citation_signature","submit_replication":"https://pith.science/pith/7CFXNEPWO3AGUFJMQ6W2HNNYQ3/action/replication_record"}},"created_at":"2026-05-18T02:22:19.796732+00:00","updated_at":"2026-05-18T02:22:19.796732+00:00"}