{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WGB354BMFAAH6DLCJQG7KBVKYH","short_pith_number":"pith:WGB354BM","schema_version":"1.0","canonical_sha256":"b183bef02c28007f0d624c0df506aac1cc264058ad3464ab7a1cad081b846e83","source":{"kind":"arxiv","id":"1411.7818","version":1},"attestation_state":"computed","paper":{"title":"On Perfect and Quasiperfect Domination in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carmen Hernando, Ignacio M. Pelayo, Jos\\'e C\\'aceres, Mar\\'ia Luz Puertas, Merc\\`e Mora","submitted_at":"2014-11-28T11:21:32Z","abstract_excerpt":"A subset $S\\subseteq V$ in a graph $G=(V,E)$ is a $k$-quasiperfect dominating set (for $k\\geq 1$) if every vertex not in $S$ is adjacent to at least one and at most $k$ vertices in $S$. The cardinality of a minimum $k$-quasiperfect dominating set in $G$ is denoted by $\\gamma_ {\\stackrel{}{1k}}(G)$. Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept and allow us to construct a decreasing chain of quasiperfect dominating numbers $ n \\ge \\gamma_ {\\stackrel{}{11}}(G) \\ge \\gamma_ {\\stackrel{}{12}}(G)\\ge \\ldots \\ge \\gamma_ {\\stackrel{}{1\\"},"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":"1411.7818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-28T11:21:32Z","cross_cats_sorted":[],"title_canon_sha256":"d63f5639c589dd245ee60c1d2b7479f5bb554dc2e244d76b064ff7760bd9da41","abstract_canon_sha256":"8275d75993392d07c558125d0d2784a7f4387b3b7a6d14d3e66c06ceeaa95fc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:37.186173Z","signature_b64":"W9Vw58ld35ZM9rhYeP8LSyijz273sLJ2Bu2AuMvEJxkHQE+2YyC73BqyGepYUgvY3ZJNgq5QbUxtNqwG1lSYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b183bef02c28007f0d624c0df506aac1cc264058ad3464ab7a1cad081b846e83","last_reissued_at":"2026-05-18T02:32:37.185754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:37.185754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Perfect and Quasiperfect Domination in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carmen Hernando, Ignacio M. Pelayo, Jos\\'e C\\'aceres, Mar\\'ia Luz Puertas, Merc\\`e Mora","submitted_at":"2014-11-28T11:21:32Z","abstract_excerpt":"A subset $S\\subseteq V$ in a graph $G=(V,E)$ is a $k$-quasiperfect dominating set (for $k\\geq 1$) if every vertex not in $S$ is adjacent to at least one and at most $k$ vertices in $S$. The cardinality of a minimum $k$-quasiperfect dominating set in $G$ is denoted by $\\gamma_ {\\stackrel{}{1k}}(G)$. Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept and allow us to construct a decreasing chain of quasiperfect dominating numbers $ n \\ge \\gamma_ {\\stackrel{}{11}}(G) \\ge \\gamma_ {\\stackrel{}{12}}(G)\\ge \\ldots \\ge \\gamma_ {\\stackrel{}{1\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7818","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":"1411.7818","created_at":"2026-05-18T02:32:37.185828+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.7818v1","created_at":"2026-05-18T02:32:37.185828+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7818","created_at":"2026-05-18T02:32:37.185828+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGB354BMFAAH","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGB354BMFAAH6DLC","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGB354BM","created_at":"2026-05-18T12:28:54.890064+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/WGB354BMFAAH6DLCJQG7KBVKYH","json":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH.json","graph_json":"https://pith.science/api/pith-number/WGB354BMFAAH6DLCJQG7KBVKYH/graph.json","events_json":"https://pith.science/api/pith-number/WGB354BMFAAH6DLCJQG7KBVKYH/events.json","paper":"https://pith.science/paper/WGB354BM"},"agent_actions":{"view_html":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH","download_json":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH.json","view_paper":"https://pith.science/paper/WGB354BM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.7818&json=true","fetch_graph":"https://pith.science/api/pith-number/WGB354BMFAAH6DLCJQG7KBVKYH/graph.json","fetch_events":"https://pith.science/api/pith-number/WGB354BMFAAH6DLCJQG7KBVKYH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH/action/storage_attestation","attest_author":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH/action/author_attestation","sign_citation":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH/action/citation_signature","submit_replication":"https://pith.science/pith/WGB354BMFAAH6DLCJQG7KBVKYH/action/replication_record"}},"created_at":"2026-05-18T02:32:37.185828+00:00","updated_at":"2026-05-18T02:32:37.185828+00:00"}