{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3NSKYB3H5B76MGLXUBJXVJD632","short_pith_number":"pith:3NSKYB3H","schema_version":"1.0","canonical_sha256":"db64ac0767e87fe61977a0537aa47edea7693e36558fadeac5e55e1bc5c7e882","source":{"kind":"arxiv","id":"1210.5091","version":2},"attestation_state":"computed","paper":{"title":"A few properties of the eigenvalues of normalized graph Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anirban Banerjee","submitted_at":"2012-10-18T11:12:43Z","abstract_excerpt":"Here we have investigated a few properties of the eigenvalues of normalized (geometric) graph Laplacian in different graphs. Preservation of eigenvalue 1 from a particular subgraph to the entire graph, the spectrum of the graph constructed with triangles share a common vertex have been addressed. Further using the number and degrees of common neighbors between vertices some new upper bounds for the largest eigenvalue have been introduced."},"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":"1210.5091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-18T11:12:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"727b74f54a98464779bdd4c68c28a4c50711fa3c659ca7f0507a6f4f1e66e994","abstract_canon_sha256":"2d69ea84d2ad6180bbd72edf47f7a105bd158f91d5c68c71065089887b37667f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:00.128745Z","signature_b64":"APNQ+v7Y3cFTFL8Bs5HVE2ngqiO5w+1fKsnssIPeZ9+PaLTFr2Q84UvX4UT7R/4NxuGFCNynnPbCUwBCk8B5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db64ac0767e87fe61977a0537aa47edea7693e36558fadeac5e55e1bc5c7e882","last_reissued_at":"2026-05-18T02:57:00.128253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:00.128253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A few properties of the eigenvalues of normalized graph Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anirban Banerjee","submitted_at":"2012-10-18T11:12:43Z","abstract_excerpt":"Here we have investigated a few properties of the eigenvalues of normalized (geometric) graph Laplacian in different graphs. Preservation of eigenvalue 1 from a particular subgraph to the entire graph, the spectrum of the graph constructed with triangles share a common vertex have been addressed. Further using the number and degrees of common neighbors between vertices some new upper bounds for the largest eigenvalue have been introduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5091","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":"1210.5091","created_at":"2026-05-18T02:57:00.128324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5091v2","created_at":"2026-05-18T02:57:00.128324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5091","created_at":"2026-05-18T02:57:00.128324+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NSKYB3H5B76","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NSKYB3H5B76MGLX","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NSKYB3H","created_at":"2026-05-18T12:26:53.410803+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/3NSKYB3H5B76MGLXUBJXVJD632","json":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632.json","graph_json":"https://pith.science/api/pith-number/3NSKYB3H5B76MGLXUBJXVJD632/graph.json","events_json":"https://pith.science/api/pith-number/3NSKYB3H5B76MGLXUBJXVJD632/events.json","paper":"https://pith.science/paper/3NSKYB3H"},"agent_actions":{"view_html":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632","download_json":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632.json","view_paper":"https://pith.science/paper/3NSKYB3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5091&json=true","fetch_graph":"https://pith.science/api/pith-number/3NSKYB3H5B76MGLXUBJXVJD632/graph.json","fetch_events":"https://pith.science/api/pith-number/3NSKYB3H5B76MGLXUBJXVJD632/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632/action/storage_attestation","attest_author":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632/action/author_attestation","sign_citation":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632/action/citation_signature","submit_replication":"https://pith.science/pith/3NSKYB3H5B76MGLXUBJXVJD632/action/replication_record"}},"created_at":"2026-05-18T02:57:00.128324+00:00","updated_at":"2026-05-18T02:57:00.128324+00:00"}