{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LLEMQ2DOHI4PEIUVQJ5CI4JOMG","short_pith_number":"pith:LLEMQ2DO","schema_version":"1.0","canonical_sha256":"5ac8c8686e3a38f22295827a24712e61bee31ba6860857e115191fcf8ea85498","source":{"kind":"arxiv","id":"1504.04225","version":1},"attestation_state":"computed","paper":{"title":"On the second largest distance eigenvalue of a graph","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Xue, Litao Guo, Ruifang Liu","submitted_at":"2015-04-16T13:39:08Z","abstract_excerpt":"Let $G$ be a simple connected graph of order $n$ and $D(G)$ be the distance matrix of $G.$ Suppose that $\\lambda_{1}(D(G))\\geq\\lambda_{2}(D(G))\\geq\\cdots\\geq\\lambda_{n}(D(G))$ are the distance spectrum of $G$. A graph $G$ is said to be determined by its $D$-spectrum if with respect to the distance matrix $D(G)$, any graph with the same spectrum as $G$ is isomorphic to $G$. In this paper, we consider spectral characterization on the second largest distance eigenvalue $\\lambda_{2}(D(G))$ of graphs, and prove that the graphs with $\\lambda_{2}(D(G))\\leq\\frac{17-\\sqrt{329}}{2}\\approx-0.5692$ are de"},"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":"1504.04225","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2015-04-16T13:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"cf66dd4bb0af1ce6db53a4389c3f59e5c28b80a52e77c75cafadbd2311f44613","abstract_canon_sha256":"5fa761480b6a900dd385d2ece42bbc0756e8c3ecef80ca2d93d12f08bd44cff0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:39.479750Z","signature_b64":"9UTmsOjBOwA6MGnEHoi3VEqtdE11TWokpnzA3hzLuO3i2vvneKO01zlCRrnNLpOEV8rGOZvH4eHJgdYgm02LDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ac8c8686e3a38f22295827a24712e61bee31ba6860857e115191fcf8ea85498","last_reissued_at":"2026-05-18T02:18:39.479184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:39.479184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the second largest distance eigenvalue of a graph","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Xue, Litao Guo, Ruifang Liu","submitted_at":"2015-04-16T13:39:08Z","abstract_excerpt":"Let $G$ be a simple connected graph of order $n$ and $D(G)$ be the distance matrix of $G.$ Suppose that $\\lambda_{1}(D(G))\\geq\\lambda_{2}(D(G))\\geq\\cdots\\geq\\lambda_{n}(D(G))$ are the distance spectrum of $G$. A graph $G$ is said to be determined by its $D$-spectrum if with respect to the distance matrix $D(G)$, any graph with the same spectrum as $G$ is isomorphic to $G$. In this paper, we consider spectral characterization on the second largest distance eigenvalue $\\lambda_{2}(D(G))$ of graphs, and prove that the graphs with $\\lambda_{2}(D(G))\\leq\\frac{17-\\sqrt{329}}{2}\\approx-0.5692$ are de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04225","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":"1504.04225","created_at":"2026-05-18T02:18:39.479282+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04225v1","created_at":"2026-05-18T02:18:39.479282+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04225","created_at":"2026-05-18T02:18:39.479282+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLEMQ2DOHI4P","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLEMQ2DOHI4PEIUV","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLEMQ2DO","created_at":"2026-05-18T12:29:29.992203+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/LLEMQ2DOHI4PEIUVQJ5CI4JOMG","json":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG.json","graph_json":"https://pith.science/api/pith-number/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/graph.json","events_json":"https://pith.science/api/pith-number/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/events.json","paper":"https://pith.science/paper/LLEMQ2DO"},"agent_actions":{"view_html":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG","download_json":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG.json","view_paper":"https://pith.science/paper/LLEMQ2DO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04225&json=true","fetch_graph":"https://pith.science/api/pith-number/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/graph.json","fetch_events":"https://pith.science/api/pith-number/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/action/storage_attestation","attest_author":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/action/author_attestation","sign_citation":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/action/citation_signature","submit_replication":"https://pith.science/pith/LLEMQ2DOHI4PEIUVQJ5CI4JOMG/action/replication_record"}},"created_at":"2026-05-18T02:18:39.479282+00:00","updated_at":"2026-05-18T02:18:39.479282+00:00"}