{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NHZUQKA6K2S6N52CQVL4RZJUEQ","short_pith_number":"pith:NHZUQKA6","schema_version":"1.0","canonical_sha256":"69f348281e56a5e6f7428557c8e5342434d85d418d37b53b14c597e46ebcfb2e","source":{"kind":"arxiv","id":"1210.1836","version":1},"attestation_state":"computed","paper":{"title":"Distance magic labeling and two products of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aleksandra Tepeh, Iztok Peterin, Marcin Anholcer, Sylwia Cichacz","submitted_at":"2012-10-05T19:00:37Z","abstract_excerpt":"Let $G=(V,E)$ be a graph of order $n$. A distance magic labeling of $G$ is a bijection $\\ell \\colon V\\rightarrow {1,...,n}$ for which there exists a positive integer $k$ such that $\\sum_{x\\in N(v)}\\ell (x)=k$ for all $v\\in V $, where $N(v)$ is the neighborhood of $v$. We introduce a natural subclass of distance magic graphs. For this class we show that it is closed for the direct product with regular graphs and closed as a second factor for lexicographic product with regular graphs. In addition, we characterize distance magic graphs among direct product of two cycles."},"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":"1210.1836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-05T19:00:37Z","cross_cats_sorted":[],"title_canon_sha256":"5eca0cc4a869edfc1a657ebed2d5aa68b2682571214ac0d76a1c9c8ef7c90e9b","abstract_canon_sha256":"85f3a46cf60e0ed4453ac73917fd66aaa31d15604f865a673a6da7c07c16f26c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:05.820998Z","signature_b64":"m6wgCmdOUIDweZHZ8gIm78opQj33mrSnXrDAv89ie0XHs9PObmgNsmsu27bnj580kAlExU8Use9luSdWEuAdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69f348281e56a5e6f7428557c8e5342434d85d418d37b53b14c597e46ebcfb2e","last_reissued_at":"2026-05-18T01:34:05.820490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:05.820490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distance magic labeling and two products of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aleksandra Tepeh, Iztok Peterin, Marcin Anholcer, Sylwia Cichacz","submitted_at":"2012-10-05T19:00:37Z","abstract_excerpt":"Let $G=(V,E)$ be a graph of order $n$. A distance magic labeling of $G$ is a bijection $\\ell \\colon V\\rightarrow {1,...,n}$ for which there exists a positive integer $k$ such that $\\sum_{x\\in N(v)}\\ell (x)=k$ for all $v\\in V $, where $N(v)$ is the neighborhood of $v$. We introduce a natural subclass of distance magic graphs. For this class we show that it is closed for the direct product with regular graphs and closed as a second factor for lexicographic product with regular graphs. In addition, we characterize distance magic graphs among direct product of two cycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1836","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":"1210.1836","created_at":"2026-05-18T01:34:05.820564+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.1836v1","created_at":"2026-05-18T01:34:05.820564+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1836","created_at":"2026-05-18T01:34:05.820564+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHZUQKA6K2S6","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHZUQKA6K2S6N52C","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHZUQKA6","created_at":"2026-05-18T12:27:16.716162+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/NHZUQKA6K2S6N52CQVL4RZJUEQ","json":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ.json","graph_json":"https://pith.science/api/pith-number/NHZUQKA6K2S6N52CQVL4RZJUEQ/graph.json","events_json":"https://pith.science/api/pith-number/NHZUQKA6K2S6N52CQVL4RZJUEQ/events.json","paper":"https://pith.science/paper/NHZUQKA6"},"agent_actions":{"view_html":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ","download_json":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ.json","view_paper":"https://pith.science/paper/NHZUQKA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.1836&json=true","fetch_graph":"https://pith.science/api/pith-number/NHZUQKA6K2S6N52CQVL4RZJUEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/NHZUQKA6K2S6N52CQVL4RZJUEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ/action/storage_attestation","attest_author":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ/action/author_attestation","sign_citation":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ/action/citation_signature","submit_replication":"https://pith.science/pith/NHZUQKA6K2S6N52CQVL4RZJUEQ/action/replication_record"}},"created_at":"2026-05-18T01:34:05.820564+00:00","updated_at":"2026-05-18T01:34:05.820564+00:00"}