{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:36HCF46OKGVFPV4PIC4NATPPZ4","short_pith_number":"pith:36HCF46O","schema_version":"1.0","canonical_sha256":"df8e22f3ce51aa57d78f40b8d04defcf1de463ad988ef500299e5adecf74ee61","source":{"kind":"arxiv","id":"1805.02437","version":1},"attestation_state":"computed","paper":{"title":"The generalized connectivity of $(n,k)$-bubble-sort graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lidong Wu, Rong-Xia Hao, Shu-Li Zhao","submitted_at":"2018-05-07T10:53:21Z","abstract_excerpt":"Let $S\\subseteq V(G)$ and $\\kappa_{G}(S)$ denote the maximum number $r$ of edge-disjoint trees $T_1, T_2, \\cdots, T_r$ in $G$ such that $V(T_i)\\bigcap V(T_{j})=S$ for any $i, j \\in \\{1, 2, \\cdots, r\\}$ and $i\\neq j$. For an integer $k$ with $2\\leq k\\leq n$, the {\\em generalized $k$-connectivity} of a graph $G$ is defined as $\\kappa_{k}(G)= min\\{\\kappa_{G}(S)|S\\subseteq V(G)$ and $|S|=k\\}$. The generalized $k$-connectivity is a generalization of the traditional connectivity. In this paper, the generalized $3$-connectivity of the $(n,k)$-bubble-sort graph $B_{n,k}$ is studied for $2\\leq k\\leq n-"},"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":"1805.02437","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-07T10:53:21Z","cross_cats_sorted":[],"title_canon_sha256":"8622e8870a206a22053f54e9a1c6276bfedfac74fd0d4e9af1114761e5e40b2e","abstract_canon_sha256":"9a91f2545d052066049b7f4d04c17191d8dc20ed768114f1f13c719c705baf01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:39.902301Z","signature_b64":"aesJNokNKWYenoGM3tktAjTjz4UWdpvPhffBd76Fdw3xpThOwkm1NFqePGYh7U9YHUkxDrntmvXBRFwCKWkkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df8e22f3ce51aa57d78f40b8d04defcf1de463ad988ef500299e5adecf74ee61","last_reissued_at":"2026-05-18T00:16:39.901830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:39.901830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The generalized connectivity of $(n,k)$-bubble-sort graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lidong Wu, Rong-Xia Hao, Shu-Li Zhao","submitted_at":"2018-05-07T10:53:21Z","abstract_excerpt":"Let $S\\subseteq V(G)$ and $\\kappa_{G}(S)$ denote the maximum number $r$ of edge-disjoint trees $T_1, T_2, \\cdots, T_r$ in $G$ such that $V(T_i)\\bigcap V(T_{j})=S$ for any $i, j \\in \\{1, 2, \\cdots, r\\}$ and $i\\neq j$. For an integer $k$ with $2\\leq k\\leq n$, the {\\em generalized $k$-connectivity} of a graph $G$ is defined as $\\kappa_{k}(G)= min\\{\\kappa_{G}(S)|S\\subseteq V(G)$ and $|S|=k\\}$. The generalized $k$-connectivity is a generalization of the traditional connectivity. In this paper, the generalized $3$-connectivity of the $(n,k)$-bubble-sort graph $B_{n,k}$ is studied for $2\\leq k\\leq n-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02437","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":"1805.02437","created_at":"2026-05-18T00:16:39.901909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.02437v1","created_at":"2026-05-18T00:16:39.901909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02437","created_at":"2026-05-18T00:16:39.901909+00:00"},{"alias_kind":"pith_short_12","alias_value":"36HCF46OKGVF","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"36HCF46OKGVFPV4P","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"36HCF46O","created_at":"2026-05-18T12:32:02.567920+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/36HCF46OKGVFPV4PIC4NATPPZ4","json":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4.json","graph_json":"https://pith.science/api/pith-number/36HCF46OKGVFPV4PIC4NATPPZ4/graph.json","events_json":"https://pith.science/api/pith-number/36HCF46OKGVFPV4PIC4NATPPZ4/events.json","paper":"https://pith.science/paper/36HCF46O"},"agent_actions":{"view_html":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4","download_json":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4.json","view_paper":"https://pith.science/paper/36HCF46O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.02437&json=true","fetch_graph":"https://pith.science/api/pith-number/36HCF46OKGVFPV4PIC4NATPPZ4/graph.json","fetch_events":"https://pith.science/api/pith-number/36HCF46OKGVFPV4PIC4NATPPZ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4/action/storage_attestation","attest_author":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4/action/author_attestation","sign_citation":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4/action/citation_signature","submit_replication":"https://pith.science/pith/36HCF46OKGVFPV4PIC4NATPPZ4/action/replication_record"}},"created_at":"2026-05-18T00:16:39.901909+00:00","updated_at":"2026-05-18T00:16:39.901909+00:00"}