{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PTBNAMHKMUCYSS7Y567YNJXQCS","short_pith_number":"pith:PTBNAMHK","schema_version":"1.0","canonical_sha256":"7cc2d030ea6505894bf8efbf86a6f0148ca1cb4e4ba61d35b35fce92f493560e","source":{"kind":"arxiv","id":"1808.10018","version":1},"attestation_state":"computed","paper":{"title":"Note on the group edge irregularity strength of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcin Anholcer, Sylwia Cichacz","submitted_at":"2018-08-29T19:30:48Z","abstract_excerpt":"We investigate the \\textit{edge group irregularity strength} ($es_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\\mathcal{G}$ of order $s$, there exists a function $f:V(G)\\rightarrow \\mathcal{G}$ such that the sums of vertex labels at every edge are distinct. In this note we provide some upper bounds on $es_g(G)$ as well as for edge irregularity strength $es(G)$ and harmonious order $\\rm{har}(G)$."},"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":"1808.10018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T19:30:48Z","cross_cats_sorted":[],"title_canon_sha256":"c94689cf750627e3a8dae7e165b2a2a1e32b1de9b4abe3ace59b01553b47d771","abstract_canon_sha256":"24496da4e0b4ed57497871817f932ad975516fbc50ba8684479e884c4be74753"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:50.125810Z","signature_b64":"ErabdRW0LG6bH5qqjxejo6NCqz8fLOT6Y4J+e1V7hEP5hkHw4gOGRs9XmNydNRNxwehS0xHUOhwfl/H8z04MDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cc2d030ea6505894bf8efbf86a6f0148ca1cb4e4ba61d35b35fce92f493560e","last_reissued_at":"2026-05-18T00:06:50.125068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:50.125068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Note on the group edge irregularity strength of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcin Anholcer, Sylwia Cichacz","submitted_at":"2018-08-29T19:30:48Z","abstract_excerpt":"We investigate the \\textit{edge group irregularity strength} ($es_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\\mathcal{G}$ of order $s$, there exists a function $f:V(G)\\rightarrow \\mathcal{G}$ such that the sums of vertex labels at every edge are distinct. In this note we provide some upper bounds on $es_g(G)$ as well as for edge irregularity strength $es(G)$ and harmonious order $\\rm{har}(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10018","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":"1808.10018","created_at":"2026-05-18T00:06:50.125195+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.10018v1","created_at":"2026-05-18T00:06:50.125195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10018","created_at":"2026-05-18T00:06:50.125195+00:00"},{"alias_kind":"pith_short_12","alias_value":"PTBNAMHKMUCY","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PTBNAMHKMUCYSS7Y","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PTBNAMHK","created_at":"2026-05-18T12:32:46.962924+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/PTBNAMHKMUCYSS7Y567YNJXQCS","json":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS.json","graph_json":"https://pith.science/api/pith-number/PTBNAMHKMUCYSS7Y567YNJXQCS/graph.json","events_json":"https://pith.science/api/pith-number/PTBNAMHKMUCYSS7Y567YNJXQCS/events.json","paper":"https://pith.science/paper/PTBNAMHK"},"agent_actions":{"view_html":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS","download_json":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS.json","view_paper":"https://pith.science/paper/PTBNAMHK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.10018&json=true","fetch_graph":"https://pith.science/api/pith-number/PTBNAMHKMUCYSS7Y567YNJXQCS/graph.json","fetch_events":"https://pith.science/api/pith-number/PTBNAMHKMUCYSS7Y567YNJXQCS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS/action/storage_attestation","attest_author":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS/action/author_attestation","sign_citation":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS/action/citation_signature","submit_replication":"https://pith.science/pith/PTBNAMHKMUCYSS7Y567YNJXQCS/action/replication_record"}},"created_at":"2026-05-18T00:06:50.125195+00:00","updated_at":"2026-05-18T00:06:50.125195+00:00"}