{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GIESKUKKROHTLSM4S22ZE6H2PH","short_pith_number":"pith:GIESKUKK","schema_version":"1.0","canonical_sha256":"320925514a8b8f35c99c96b59278fa79df4c0d68b0825bd6725be908b3831865","source":{"kind":"arxiv","id":"1206.6327","version":1},"attestation_state":"computed","paper":{"title":"The Radio numbers of all graphs of order $n$ and diameter $n-2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Katherine Benson, Maggy Tomova, Matthew Porter","submitted_at":"2012-06-27T16:23:43Z","abstract_excerpt":"A radio labeling of a connected graph $G$ is a function $c:V(G) \\to \\mathbb Z_+$ such that for every two distinct vertices $u$ and $v$ of $G$ $$\\text{distance}(u,v)+|c(u)-c(v)|\\geq 1+ \\text{diameter}(G).$$ The radio number of a graph $G$ is the smallest integer $M$ for which there exists a labeling $c$ with $c(v)\\leq M$ for all $v\\in V(G)$. The radio number of graphs of order $n$ and diameter $n-1$, i.e., paths, was determined in \\cite{paths}. Here we determine the radio numbers of all graphs of order $n$ and diameter $n-2$."},"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":"1206.6327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-27T16:23:43Z","cross_cats_sorted":[],"title_canon_sha256":"079bd3ec49fdb4ddd45f2645674b559fb2380d9eedc028d794ab759298713c95","abstract_canon_sha256":"82245cc4fceb6070207ff3fad863733fa2f093a02d26c29bfee6a585a4bb10f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:26.953361Z","signature_b64":"UgNE+UYO7ztA+0ZWUXVz1hQP2g908j1tKgm/S9mrdHGlJAmHBronDAspaFe2VqZRDpX+jhPyUXUMfrmSAwqODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"320925514a8b8f35c99c96b59278fa79df4c0d68b0825bd6725be908b3831865","last_reissued_at":"2026-05-18T03:52:26.952652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:26.952652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Radio numbers of all graphs of order $n$ and diameter $n-2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Katherine Benson, Maggy Tomova, Matthew Porter","submitted_at":"2012-06-27T16:23:43Z","abstract_excerpt":"A radio labeling of a connected graph $G$ is a function $c:V(G) \\to \\mathbb Z_+$ such that for every two distinct vertices $u$ and $v$ of $G$ $$\\text{distance}(u,v)+|c(u)-c(v)|\\geq 1+ \\text{diameter}(G).$$ The radio number of a graph $G$ is the smallest integer $M$ for which there exists a labeling $c$ with $c(v)\\leq M$ for all $v\\in V(G)$. The radio number of graphs of order $n$ and diameter $n-1$, i.e., paths, was determined in \\cite{paths}. Here we determine the radio numbers of all graphs of order $n$ and diameter $n-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6327","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":"1206.6327","created_at":"2026-05-18T03:52:26.952773+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.6327v1","created_at":"2026-05-18T03:52:26.952773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6327","created_at":"2026-05-18T03:52:26.952773+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIESKUKKROHT","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIESKUKKROHTLSM4","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIESKUKK","created_at":"2026-05-18T12:27:06.952714+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/GIESKUKKROHTLSM4S22ZE6H2PH","json":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH.json","graph_json":"https://pith.science/api/pith-number/GIESKUKKROHTLSM4S22ZE6H2PH/graph.json","events_json":"https://pith.science/api/pith-number/GIESKUKKROHTLSM4S22ZE6H2PH/events.json","paper":"https://pith.science/paper/GIESKUKK"},"agent_actions":{"view_html":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH","download_json":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH.json","view_paper":"https://pith.science/paper/GIESKUKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.6327&json=true","fetch_graph":"https://pith.science/api/pith-number/GIESKUKKROHTLSM4S22ZE6H2PH/graph.json","fetch_events":"https://pith.science/api/pith-number/GIESKUKKROHTLSM4S22ZE6H2PH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH/action/storage_attestation","attest_author":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH/action/author_attestation","sign_citation":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH/action/citation_signature","submit_replication":"https://pith.science/pith/GIESKUKKROHTLSM4S22ZE6H2PH/action/replication_record"}},"created_at":"2026-05-18T03:52:26.952773+00:00","updated_at":"2026-05-18T03:52:26.952773+00:00"}