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Hansen used the AutoGraphiX and made the following conjecture about the revised Szeged index for a connected bicyclic graph $G$ of order $n \\geq 6$: $$ Sz^*(G)\\leq \\{{array}{ll} (n^3+n^2-n-1)/4,& {if $n$ is odd}, (n"},"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":"1104.2122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-12T06:53:16Z","cross_cats_sorted":[],"title_canon_sha256":"a86c8054a43469d3cd705eeaad22d338e09b9e04bd2da747058c58dc9f519ac3","abstract_canon_sha256":"e39169b029767ecbeb9598ad7bff1efda122bfdb6abe6a08687bface6baca5b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:35.874938Z","signature_b64":"hlqnjiBXnNcQ/MC74KrYe5sDZLLgwvIAkrgWXXx4u1G6RziRc0/xMMKiofWExQa7XkLPthkbXvr55ciBzHteDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c5f8e158f6c4e2a5aeec610c9d24ed58c135ce69d17c03fdbd38a57bde430fb","last_reissued_at":"2026-05-18T04:24:35.874418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:35.874418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bicyclic graphs with maximal revised Szeged index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mengmeng Liu, Xueliang Li","submitted_at":"2011-04-12T06:53:16Z","abstract_excerpt":"The revised Szeged index $Sz^*(G)$ is defined as $Sz^*(G)=\\sum_{e=uv \\in E}(n_u(e)+ n_0(e)/2)(n_v(e)+ n_0(e)/2),$ where $n_u(e)$ and $n_v(e)$ are, respectively, the number of vertices of $G$ lying closer to vertex $u$ than to vertex $v$ and the number of vertices of $G$ lying closer to vertex $v$ than to vertex $u$, and $n_0(e)$ is the number of vertices equidistant to $u$ and $v$. Hansen used the AutoGraphiX and made the following conjecture about the revised Szeged index for a connected bicyclic graph $G$ of order $n \\geq 6$: $$ Sz^*(G)\\leq \\{{array}{ll} (n^3+n^2-n-1)/4,& {if $n$ is odd}, (n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2122","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":"1104.2122","created_at":"2026-05-18T04:24:35.874504+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.2122v1","created_at":"2026-05-18T04:24:35.874504+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2122","created_at":"2026-05-18T04:24:35.874504+00:00"},{"alias_kind":"pith_short_12","alias_value":"TRPY4FMPNRHC","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TRPY4FMPNRHCUWXO","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TRPY4FMP","created_at":"2026-05-18T12:26:42.757692+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/TRPY4FMPNRHCUWXOYYIMTUSO2W","json":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W.json","graph_json":"https://pith.science/api/pith-number/TRPY4FMPNRHCUWXOYYIMTUSO2W/graph.json","events_json":"https://pith.science/api/pith-number/TRPY4FMPNRHCUWXOYYIMTUSO2W/events.json","paper":"https://pith.science/paper/TRPY4FMP"},"agent_actions":{"view_html":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W","download_json":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W.json","view_paper":"https://pith.science/paper/TRPY4FMP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.2122&json=true","fetch_graph":"https://pith.science/api/pith-number/TRPY4FMPNRHCUWXOYYIMTUSO2W/graph.json","fetch_events":"https://pith.science/api/pith-number/TRPY4FMPNRHCUWXOYYIMTUSO2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W/action/storage_attestation","attest_author":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W/action/author_attestation","sign_citation":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W/action/citation_signature","submit_replication":"https://pith.science/pith/TRPY4FMPNRHCUWXOYYIMTUSO2W/action/replication_record"}},"created_at":"2026-05-18T04:24:35.874504+00:00","updated_at":"2026-05-18T04:24:35.874504+00:00"}