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An integer additive set-indexer (IASI) of a given graph $G$ is an injective function $f:V(G)\\to \\mathcal{P}(\\mathbb{N}_0)$ such that the induced function $f^+:E(G) \\to \\mathcal{P}(\\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ of a graph $G$ is said to be a weak IASI of $G$ if $|f^+(uv)|=\\max(|f(u)|,|f(v)|)$ for all $u,v\\in V(G)$. A graph which admits a weak IASI may be called a weak IASI graph. The sparing number of a graph $G$ is the minimum numbe"},"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":"1505.03841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-05-11T10:44:04Z","cross_cats_sorted":[],"title_canon_sha256":"7dbba6c90219fd86e347de91793f99f9b908583117b970826f76cb7c3b3adb4b","abstract_canon_sha256":"2b0e37a49c5f2bcd285979ddf7a81ebe08cb23b6f72a131f4792cbb0b45504fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:52.874606Z","signature_b64":"6O/ae0Y6+JIHzde+G/vNK1cizd2E0gpQu0H5WAPnkpn01gFVJPUKbWtbMhpbKhfBjWN7xtmbh8yMQUpje4hODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e84dd79ff911f033ad023f340c71dc012ecca03683b8a2bb9b7a8aa5890b8588","last_reissued_at":"2026-05-18T02:09:52.873840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:52.873840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on the Sparing Number of the Sieve Graphs of Certain Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Augustine Germina, Naduvath Sudev","submitted_at":"2015-05-11T10:44:04Z","abstract_excerpt":"Let $\\mathbb{N}_0$ denote the set of all non-negative integers and $\\mathcal{P}(\\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) of a given graph $G$ is an injective function $f:V(G)\\to \\mathcal{P}(\\mathbb{N}_0)$ such that the induced function $f^+:E(G) \\to \\mathcal{P}(\\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ of a graph $G$ is said to be a weak IASI of $G$ if $|f^+(uv)|=\\max(|f(u)|,|f(v)|)$ for all $u,v\\in V(G)$. A graph which admits a weak IASI may be called a weak IASI graph. 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