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An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\\rightarrow \\mathcal{P}(\\mathbb{N}_0)$ such that the induced function $f^+:E(G) \\rightarrow \\mathcal{P}(\\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$ and $\\mathcal{P}(\\mathbb{N}_0)$ is the power set of $\\mathbb{N}_0$. If $f^+(uv)=k \\forall ~ uv\\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak int"},"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":"1407.4869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-18T02:00:10Z","cross_cats_sorted":[],"title_canon_sha256":"53f598cb17a71fc5969d90aa09b3217fb8f46719167286f9bab1c1e310326f8a","abstract_canon_sha256":"6d3cb644abe9ac1d72d510566455bd8b5bcde47be1d7e55a15e904dd0ee0f67a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:22.512196Z","signature_b64":"Mc+IoUgl3LgDuO8kWh/JNiUjXFzImLyWocVR4a9XJnEO7AScfdzUOjGuof5xiYT2UwSjL058eBrxRqp+wNbRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64f9a7aa51a41c771ac41b1cfe5fa4f801d7fde00d452dafa03a7ecb3be37b97","last_reissued_at":"2026-05-18T02:47:22.511527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:22.511527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Sparing Number of the Cartesian Products of Certain Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"K. A. Germina, K. P. Chithra, N. K. Sudev","submitted_at":"2014-07-18T02:00:10Z","abstract_excerpt":"Let $\\mathbb{N}_0$ be the set of all non-negative integers. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\\rightarrow \\mathcal{P}(\\mathbb{N}_0)$ such that the induced function $f^+:E(G) \\rightarrow \\mathcal{P}(\\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$ and $\\mathcal{P}(\\mathbb{N}_0)$ is the power set of $\\mathbb{N}_0$. If $f^+(uv)=k \\forall ~ uv\\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. 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