{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A5PL63Z5JFPKXGIZJAV3A4VSBY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4c78d71fb445f5e635fc84676a2f586bf8b1e6032a677e7d729c46546888d0de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-06T06:21:30Z","title_canon_sha256":"3429e64de45abd05c4d4fed44fd67b0cb6df5d174010a6a30a779f22f1d57004"},"schema_version":"1.0","source":{"id":"1609.01406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01406","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01406v1","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01406","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"A5PL63Z5JFPK","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A5PL63Z5JFPKXGIZ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A5PL63Z5","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:25753e1e7c0aaab7a481ce8b37593aac4bc46cc4dd5d753b32ad6b2484d66a62","target":"graph","created_at":"2026-05-18T01:05:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The atom-bond connectivity (ABC) index is a well-known degree-based molecular structure descriptor with a variety of chemical applications. In 2010 Graovac and Ghorbani introduced a distance-based analog of this index, the Graovac-Ghorbani (GG) index, which yielded promising results when compared to analogous descriptors. In this paper, we investigate the structure of graphs that maximize and minimize the GG index. Specifically, we show that amongst all bipartite graphs, the minimum GG index is attained by a complete bipartite graph, while the maximum GG index is attained by a path or a cycle-","authors_text":"Barbara Ikica, Darko Dimitrov, Riste \\v{S}krekovski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-06T06:21:30Z","title":"Remarks on the Graovac-Ghorbani index of bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01406","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2a528fe0985b3839ceea871b0582529cca1985581a61e4f48e283b0fc5e1ff1f","target":"record","created_at":"2026-05-18T01:05:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4c78d71fb445f5e635fc84676a2f586bf8b1e6032a677e7d729c46546888d0de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-06T06:21:30Z","title_canon_sha256":"3429e64de45abd05c4d4fed44fd67b0cb6df5d174010a6a30a779f22f1d57004"},"schema_version":"1.0","source":{"id":"1609.01406","kind":"arxiv","version":1}},"canonical_sha256":"075ebf6f3d495eab9919482bb072b20e2c6224a69fc2e108168ee75c6cc6d212","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"075ebf6f3d495eab9919482bb072b20e2c6224a69fc2e108168ee75c6cc6d212","first_computed_at":"2026-05-18T01:05:39.665628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:39.665628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o/PeGcNRrO0tUeU5JzxvopZT1zR4xUWABQMNqfWlghJOzAF7P+5qFXhP0VY1r1IsBNCYsUoWPUXMNuzy/DW4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:39.666082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a528fe0985b3839ceea871b0582529cca1985581a61e4f48e283b0fc5e1ff1f","sha256:25753e1e7c0aaab7a481ce8b37593aac4bc46cc4dd5d753b32ad6b2484d66a62"],"state_sha256":"68849ea4e42f779401709f6dcefb3bbfe5d4f2276ed39341bfd3dad6e795d01f"}