{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5ZO3ZLIXAQENWOLD7NSLQR3SR5","short_pith_number":"pith:5ZO3ZLIX","schema_version":"1.0","canonical_sha256":"ee5dbcad170408db3963fb64b847728f77ff9fc78ca074622a4bcd0857e91b8f","source":{"kind":"arxiv","id":"1210.5649","version":1},"attestation_state":"computed","paper":{"title":"Edge-distance-regular graphs are distance-regular","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Dalf\\'o, C. Delorme, H. Suzuki, M.A. Fiol, M. C\\'amara","submitted_at":"2012-10-20T19:39:34Z","abstract_excerpt":"A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph $\\G$ is distance-regular and homogeneous. More precisely, $\\G$ is edge-distance-regular if and only if it is bipartite distance-regular or a generalized odd graph. Also, we obtain the relationships between some of their corresponding parameters, mainly, the distance polynomials and the intersection numbers."},"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":"1210.5649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-20T19:39:34Z","cross_cats_sorted":[],"title_canon_sha256":"d13ea00cb16b861f95cb25fecfbd0c850bce7b42b03de0f6b78e41113b8303ec","abstract_canon_sha256":"29bcb90a1d45ef473b1658a7ab02db638b168cec5e276aabe296bd47f9db6772"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:43.449121Z","signature_b64":"2panLgnk/40AqvFn9HNyPeaBj9gXcx7vZXhoMEllEzeIAhK0OTyhGbc4YDCjOew9W8P/f9kUjBit4kot6HkTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee5dbcad170408db3963fb64b847728f77ff9fc78ca074622a4bcd0857e91b8f","last_reissued_at":"2026-05-18T03:42:43.448506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:43.448506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge-distance-regular graphs are distance-regular","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Dalf\\'o, C. Delorme, H. Suzuki, M.A. Fiol, M. C\\'amara","submitted_at":"2012-10-20T19:39:34Z","abstract_excerpt":"A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph $\\G$ is distance-regular and homogeneous. More precisely, $\\G$ is edge-distance-regular if and only if it is bipartite distance-regular or a generalized odd graph. Also, we obtain the relationships between some of their corresponding parameters, mainly, the distance polynomials and the intersection numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5649","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":"1210.5649","created_at":"2026-05-18T03:42:43.448632+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5649v1","created_at":"2026-05-18T03:42:43.448632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5649","created_at":"2026-05-18T03:42:43.448632+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZO3ZLIXAQEN","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZO3ZLIXAQENWOLD","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZO3ZLIX","created_at":"2026-05-18T12:26:56.085431+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/5ZO3ZLIXAQENWOLD7NSLQR3SR5","json":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5.json","graph_json":"https://pith.science/api/pith-number/5ZO3ZLIXAQENWOLD7NSLQR3SR5/graph.json","events_json":"https://pith.science/api/pith-number/5ZO3ZLIXAQENWOLD7NSLQR3SR5/events.json","paper":"https://pith.science/paper/5ZO3ZLIX"},"agent_actions":{"view_html":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5","download_json":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5.json","view_paper":"https://pith.science/paper/5ZO3ZLIX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5649&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZO3ZLIXAQENWOLD7NSLQR3SR5/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZO3ZLIXAQENWOLD7NSLQR3SR5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5/action/storage_attestation","attest_author":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5/action/author_attestation","sign_citation":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5/action/citation_signature","submit_replication":"https://pith.science/pith/5ZO3ZLIXAQENWOLD7NSLQR3SR5/action/replication_record"}},"created_at":"2026-05-18T03:42:43.448632+00:00","updated_at":"2026-05-18T03:42:43.448632+00:00"}