{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LSX6U53AIXMON3BYJ53M7PMFE7","short_pith_number":"pith:LSX6U53A","schema_version":"1.0","canonical_sha256":"5cafea776045d8e6ec384f76cfbd8527fdb3625b1930661ae873b34efd2c3230","source":{"kind":"arxiv","id":"1701.00190","version":1},"attestation_state":"computed","paper":{"title":"A Study on the Product Set-Labeling of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"N. K. Sudev","submitted_at":"2017-01-01T03:46:41Z","abstract_excerpt":"Let $X$ be a non-empty ground set and $\\mathscr{P}(X)$ be its power set. A set-labeling (or a set-valuation) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\mathscr{P}(X)$ such that the induced function $f^*:E(G) \\to \\mathscr{P}(X)$ is defined by $f^*(uv)=f(u)\\ast f(v)$, where $f(u)\\ast f(v)$ is a binary operation of the sets $f(u)$ and $f(v)$. A graph which admits a set-labeling is known to be a set-labeled graph. A set-labeling $f$ of a graph $G$ is said to be a set-indexer of $G$ if the associated function $f^*$ is also injective. In this paper, we introduce a new notion name"},"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":"1701.00190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-01-01T03:46:41Z","cross_cats_sorted":[],"title_canon_sha256":"0297cfc04affd639e90b99b0044637e27684e88dc3ba1da09e669d011902e0b9","abstract_canon_sha256":"92bf39f9bb9f93d8d3ed54cca2901c4bb9e3cea69df3e4bd815f6f217fb82b98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:36.130802Z","signature_b64":"zWLL0eOU6osWsVBwHGnn9VjVfNws76M6YvuWXUdlUiq2v0yC0wh5kb0cduMTTohy+GXgzYf1/xrVEGL+ElbaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cafea776045d8e6ec384f76cfbd8527fdb3625b1930661ae873b34efd2c3230","last_reissued_at":"2026-05-18T00:53:36.130233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:36.130233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Study on the Product Set-Labeling of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"N. K. Sudev","submitted_at":"2017-01-01T03:46:41Z","abstract_excerpt":"Let $X$ be a non-empty ground set and $\\mathscr{P}(X)$ be its power set. A set-labeling (or a set-valuation) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\mathscr{P}(X)$ such that the induced function $f^*:E(G) \\to \\mathscr{P}(X)$ is defined by $f^*(uv)=f(u)\\ast f(v)$, where $f(u)\\ast f(v)$ is a binary operation of the sets $f(u)$ and $f(v)$. A graph which admits a set-labeling is known to be a set-labeled graph. A set-labeling $f$ of a graph $G$ is said to be a set-indexer of $G$ if the associated function $f^*$ is also injective. In this paper, we introduce a new notion name"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00190","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":"1701.00190","created_at":"2026-05-18T00:53:36.130306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.00190v1","created_at":"2026-05-18T00:53:36.130306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00190","created_at":"2026-05-18T00:53:36.130306+00:00"},{"alias_kind":"pith_short_12","alias_value":"LSX6U53AIXMO","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LSX6U53AIXMON3BY","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LSX6U53A","created_at":"2026-05-18T12:31:28.150371+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/LSX6U53AIXMON3BYJ53M7PMFE7","json":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7.json","graph_json":"https://pith.science/api/pith-number/LSX6U53AIXMON3BYJ53M7PMFE7/graph.json","events_json":"https://pith.science/api/pith-number/LSX6U53AIXMON3BYJ53M7PMFE7/events.json","paper":"https://pith.science/paper/LSX6U53A"},"agent_actions":{"view_html":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7","download_json":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7.json","view_paper":"https://pith.science/paper/LSX6U53A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.00190&json=true","fetch_graph":"https://pith.science/api/pith-number/LSX6U53AIXMON3BYJ53M7PMFE7/graph.json","fetch_events":"https://pith.science/api/pith-number/LSX6U53AIXMON3BYJ53M7PMFE7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7/action/storage_attestation","attest_author":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7/action/author_attestation","sign_citation":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7/action/citation_signature","submit_replication":"https://pith.science/pith/LSX6U53AIXMON3BYJ53M7PMFE7/action/replication_record"}},"created_at":"2026-05-18T00:53:36.130306+00:00","updated_at":"2026-05-18T00:53:36.130306+00:00"}