{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HVPUJITGYGT4TQ6HC36LFI72GL","short_pith_number":"pith:HVPUJITG","schema_version":"1.0","canonical_sha256":"3d5f44a266c1a7c9c3c716fcb2a3fa32db0b46064c4bacf95548f59829e3d54d","source":{"kind":"arxiv","id":"1310.7308","version":1},"attestation_state":"computed","paper":{"title":"Laplacian and signless Laplacian spectral radii of graphs with fixed domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Rundan Xing","submitted_at":"2013-10-28T04:02:35Z","abstract_excerpt":"In this paper, we determine the maximal Laplacian and signless Laplacian spectral radii for graphs with fixed number of vertices and domination number, and characterize the extremal graphs respectively."},"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":"1310.7308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-28T04:02:35Z","cross_cats_sorted":[],"title_canon_sha256":"a71fca596a1b1aed656cc01c8c46512fd079ca656e0b0988047ed90aa1425926","abstract_canon_sha256":"a4a2fb193eae8f2b083c1f0b7d84d0b87a9b481de2a9ba913761ad1341f6b1de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:45.712744Z","signature_b64":"3Inujg/qJ4lwYoeznJQw0vPXXsBUEEzMkgKQjv4DlVw1MT/3lBIAh5yMNr1HEmtjXLO+JJ+efBB6F6GCbzlRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d5f44a266c1a7c9c3c716fcb2a3fa32db0b46064c4bacf95548f59829e3d54d","last_reissued_at":"2026-05-18T03:08:45.712270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:45.712270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Laplacian and signless Laplacian spectral radii of graphs with fixed domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Rundan Xing","submitted_at":"2013-10-28T04:02:35Z","abstract_excerpt":"In this paper, we determine the maximal Laplacian and signless Laplacian spectral radii for graphs with fixed number of vertices and domination number, and characterize the extremal graphs respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7308","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":"1310.7308","created_at":"2026-05-18T03:08:45.712342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.7308v1","created_at":"2026-05-18T03:08:45.712342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7308","created_at":"2026-05-18T03:08:45.712342+00:00"},{"alias_kind":"pith_short_12","alias_value":"HVPUJITGYGT4","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HVPUJITGYGT4TQ6H","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HVPUJITG","created_at":"2026-05-18T12:27:46.883200+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/HVPUJITGYGT4TQ6HC36LFI72GL","json":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL.json","graph_json":"https://pith.science/api/pith-number/HVPUJITGYGT4TQ6HC36LFI72GL/graph.json","events_json":"https://pith.science/api/pith-number/HVPUJITGYGT4TQ6HC36LFI72GL/events.json","paper":"https://pith.science/paper/HVPUJITG"},"agent_actions":{"view_html":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL","download_json":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL.json","view_paper":"https://pith.science/paper/HVPUJITG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.7308&json=true","fetch_graph":"https://pith.science/api/pith-number/HVPUJITGYGT4TQ6HC36LFI72GL/graph.json","fetch_events":"https://pith.science/api/pith-number/HVPUJITGYGT4TQ6HC36LFI72GL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL/action/storage_attestation","attest_author":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL/action/author_attestation","sign_citation":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL/action/citation_signature","submit_replication":"https://pith.science/pith/HVPUJITGYGT4TQ6HC36LFI72GL/action/replication_record"}},"created_at":"2026-05-18T03:08:45.712342+00:00","updated_at":"2026-05-18T03:08:45.712342+00:00"}