{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KTOB5PCAO4X3Y6C4ZSTA774G6Q","short_pith_number":"pith:KTOB5PCA","schema_version":"1.0","canonical_sha256":"54dc1ebc40772fbc785ccca60fff86f42c4f304f2141e12a9acf7693ca9f99c5","source":{"kind":"arxiv","id":"1704.03122","version":1},"attestation_state":"computed","paper":{"title":"On graphs with $m(\\partial^L_1)=n-3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lu Lu, Qiongxiang Huang, Xueyi Huang","submitted_at":"2017-04-11T02:36:07Z","abstract_excerpt":"Let $\\partial^L_1\\ge\\partial^L_2\\ge\\cdots\\ge\\partial^L_n$ be the distance Laplacian eigenvalues of a connected graph $G$ and $m(\\partial^L_i)$ the multiplicity of $\\partial^L_i$. It is well known that the graphs with $m(\\partial^L_1)=n-1$ are complete graphs. Recently, the graphs with $m(\\partial^L_1)=n-2$ have been characterized by Celso et al. In this paper, we completely determine the graphs with $m(\\partial^L_1)=n-3$."},"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":"1704.03122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-11T02:36:07Z","cross_cats_sorted":[],"title_canon_sha256":"acfa5c0200946bd49e81db5e06311d56689dc7e78b986561d82c396f9a2c20ca","abstract_canon_sha256":"8fc0ef4ac4dd71b87b2471a4a5cd13df06209723c76f5aee989e11aa5f54443a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:33.466761Z","signature_b64":"aDJYhsIOI0CykcmAhnVHxrqEEnBJ/g9GBnzJx49q+gfGTIutaFchumJ+Ixa+XPVoLXormj9jA4v8hFtqVFlsAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54dc1ebc40772fbc785ccca60fff86f42c4f304f2141e12a9acf7693ca9f99c5","last_reissued_at":"2026-05-18T00:46:33.466079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:33.466079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On graphs with $m(\\partial^L_1)=n-3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lu Lu, Qiongxiang Huang, Xueyi Huang","submitted_at":"2017-04-11T02:36:07Z","abstract_excerpt":"Let $\\partial^L_1\\ge\\partial^L_2\\ge\\cdots\\ge\\partial^L_n$ be the distance Laplacian eigenvalues of a connected graph $G$ and $m(\\partial^L_i)$ the multiplicity of $\\partial^L_i$. It is well known that the graphs with $m(\\partial^L_1)=n-1$ are complete graphs. Recently, the graphs with $m(\\partial^L_1)=n-2$ have been characterized by Celso et al. In this paper, we completely determine the graphs with $m(\\partial^L_1)=n-3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03122","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":"1704.03122","created_at":"2026-05-18T00:46:33.466179+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.03122v1","created_at":"2026-05-18T00:46:33.466179+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03122","created_at":"2026-05-18T00:46:33.466179+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTOB5PCAO4X3","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTOB5PCAO4X3Y6C4","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTOB5PCA","created_at":"2026-05-18T12:31:28.150371+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/KTOB5PCAO4X3Y6C4ZSTA774G6Q","json":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q.json","graph_json":"https://pith.science/api/pith-number/KTOB5PCAO4X3Y6C4ZSTA774G6Q/graph.json","events_json":"https://pith.science/api/pith-number/KTOB5PCAO4X3Y6C4ZSTA774G6Q/events.json","paper":"https://pith.science/paper/KTOB5PCA"},"agent_actions":{"view_html":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q","download_json":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q.json","view_paper":"https://pith.science/paper/KTOB5PCA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.03122&json=true","fetch_graph":"https://pith.science/api/pith-number/KTOB5PCAO4X3Y6C4ZSTA774G6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/KTOB5PCAO4X3Y6C4ZSTA774G6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q/action/storage_attestation","attest_author":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q/action/author_attestation","sign_citation":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q/action/citation_signature","submit_replication":"https://pith.science/pith/KTOB5PCAO4X3Y6C4ZSTA774G6Q/action/replication_record"}},"created_at":"2026-05-18T00:46:33.466179+00:00","updated_at":"2026-05-18T00:46:33.466179+00:00"}