{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RVOIB7RHBHMUDAACVM2DYHC3XO","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":"26ba8707a875c1d04357b676526d0f02322c82370fb00672ec5a3429a1e32a8d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-12T02:26:47Z","title_canon_sha256":"98e4bd2fa380aef07b5dc2556b698bb5f96f9e934f7eed69c54f9446c8d84e12"},"schema_version":"1.0","source":{"id":"1204.2604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2604","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2604v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2604","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"RVOIB7RHBHMU","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RVOIB7RHBHMUDAAC","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RVOIB7RH","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:0f9de1d0996debe49afeacef4d3aabecc8012eb6dc7bf749b19476f3a2070fa3","target":"graph","created_at":"2026-05-18T03:58:03Z","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":"A routing $R$ of a given connected graph $G$ of order $n$ is a collection of $n(n-1)$ simple paths connecting every ordered pair of vertices of $G$. The vertex-forwarding index $\\xi(G,R)$ of $G$ with respect to $R$ is defined as the maximum number of paths in $R$ passing through any vertex of $G$. The vertex-forwarding index $\\xi(G)$ of $G$ is defined as the minimum $\\xi(G,R)$ over all routing $R$'s of $G$. Similarly, the edge-forwarding index $ \\pi(G,R)$ of $G$ with respect to $R$ is the maximum number of paths in $R$ passing through any edge of $G$. The edge-forwarding index $\\pi(G)$ of $G$ ","authors_text":"Jun-Ming Xu, Min Xu","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-12T02:26:47Z","title":"The Forwarding Indices of Graphs -- a Survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2604","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:b0090d91e5df1c16d2829bc0952360f6773851703d07e54d5d3ac0a7db28723b","target":"record","created_at":"2026-05-18T03:58:03Z","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":"26ba8707a875c1d04357b676526d0f02322c82370fb00672ec5a3429a1e32a8d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-12T02:26:47Z","title_canon_sha256":"98e4bd2fa380aef07b5dc2556b698bb5f96f9e934f7eed69c54f9446c8d84e12"},"schema_version":"1.0","source":{"id":"1204.2604","kind":"arxiv","version":1}},"canonical_sha256":"8d5c80fe2709d9418002ab343c1c5bbb9e78c8a3da905869cadc4ddc400243f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d5c80fe2709d9418002ab343c1c5bbb9e78c8a3da905869cadc4ddc400243f0","first_computed_at":"2026-05-18T03:58:03.928423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:03.928423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FLNxjX9/nefwePg3nWkRNSTZdEJqWwnZOxHMQVz1z8oaUCnZ7OeLfd/1Y5L095Rlrxtj9MeIhZNab9LmXjCWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:03.928841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0090d91e5df1c16d2829bc0952360f6773851703d07e54d5d3ac0a7db28723b","sha256:0f9de1d0996debe49afeacef4d3aabecc8012eb6dc7bf749b19476f3a2070fa3"],"state_sha256":"9a787f0fd514424cf8a011cba9f33e5ab7b04956fc6b1a2d1a4ac85b95b0de71"}