{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QXBPI3UK6MN5ODQZJY7NRCJAHT","short_pith_number":"pith:QXBPI3UK","schema_version":"1.0","canonical_sha256":"85c2f46e8af31bd70e194e3ed889203cdefbfd1aa2486d6b519c3129d0c7f41d","source":{"kind":"arxiv","id":"1512.08938","version":1},"attestation_state":"computed","paper":{"title":"Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edin Glogi\\'c, Emir Zogi\\'c, Ivan Gutman, Juliane Capaverde, Luiz Emilio Allem, Vilmar Trevisan","submitted_at":"2015-12-30T13:28:10Z","abstract_excerpt":"The resolvent energy of a graph $G$ of order $n$ is defined as $ER=\\sum_{i=1}^n (n-\\lambda_i)^{-1}$, where $\\lambda_1,\\lambda_2,\\ldots,\\lambda_n$ are the eigenvalues of $G$. In a recent work [Gutman et al., {\\it MATCH Commun. Math. Comput. Chem.\\/} {\\bf 75} (2016) 279--290] the structure of the graphs extremal w.r.t. $ER$ were conjectured, based on an extensive computer--aided search. We now confirm the validity of some of these conjectures."},"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":"1512.08938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-30T13:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"ad2d080d68aeca805b078c0ac792449407e8c83ed3efa318c8f1e9e11fcd8f6b","abstract_canon_sha256":"f5456ac55878ab7e0073668e5d3d27fd0f9017f87c2445ceb4a8f00e8c62a482"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:34.440787Z","signature_b64":"6spgdM37EQ/Y3XfasI4khVGSmYRTes2kA/XjtjBuyG5hw9dul50WUshPJyCmEM2ayrjpPmsiwIwLFCDZj2HTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85c2f46e8af31bd70e194e3ed889203cdefbfd1aa2486d6b519c3129d0c7f41d","last_reissued_at":"2026-05-18T01:23:34.440121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:34.440121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edin Glogi\\'c, Emir Zogi\\'c, Ivan Gutman, Juliane Capaverde, Luiz Emilio Allem, Vilmar Trevisan","submitted_at":"2015-12-30T13:28:10Z","abstract_excerpt":"The resolvent energy of a graph $G$ of order $n$ is defined as $ER=\\sum_{i=1}^n (n-\\lambda_i)^{-1}$, where $\\lambda_1,\\lambda_2,\\ldots,\\lambda_n$ are the eigenvalues of $G$. In a recent work [Gutman et al., {\\it MATCH Commun. Math. Comput. Chem.\\/} {\\bf 75} (2016) 279--290] the structure of the graphs extremal w.r.t. $ER$ were conjectured, based on an extensive computer--aided search. We now confirm the validity of some of these conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08938","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":"1512.08938","created_at":"2026-05-18T01:23:34.440221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.08938v1","created_at":"2026-05-18T01:23:34.440221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08938","created_at":"2026-05-18T01:23:34.440221+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXBPI3UK6MN5","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXBPI3UK6MN5ODQZ","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXBPI3UK","created_at":"2026-05-18T12:29:39.896362+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/QXBPI3UK6MN5ODQZJY7NRCJAHT","json":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT.json","graph_json":"https://pith.science/api/pith-number/QXBPI3UK6MN5ODQZJY7NRCJAHT/graph.json","events_json":"https://pith.science/api/pith-number/QXBPI3UK6MN5ODQZJY7NRCJAHT/events.json","paper":"https://pith.science/paper/QXBPI3UK"},"agent_actions":{"view_html":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT","download_json":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT.json","view_paper":"https://pith.science/paper/QXBPI3UK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.08938&json=true","fetch_graph":"https://pith.science/api/pith-number/QXBPI3UK6MN5ODQZJY7NRCJAHT/graph.json","fetch_events":"https://pith.science/api/pith-number/QXBPI3UK6MN5ODQZJY7NRCJAHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT/action/storage_attestation","attest_author":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT/action/author_attestation","sign_citation":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT/action/citation_signature","submit_replication":"https://pith.science/pith/QXBPI3UK6MN5ODQZJY7NRCJAHT/action/replication_record"}},"created_at":"2026-05-18T01:23:34.440221+00:00","updated_at":"2026-05-18T01:23:34.440221+00:00"}