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A weak integer additive set-labeling (WIASL) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\sP(X)-\\{\\emptyset\\}$ where induced function $f^+:E(G) \\to \\sP(X)-\\{\\emptyset\\}$ is defined by $f^+ (uv) = f(u)+ f(v)$ such that either $|f^+ (uv)|=|f(u)|$ or $|f^+ (uv)|=|f(v)|$ , where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. The sparing number of a WIASL-graph $G$ is the minimum required number of edges in $G$ having singleton set-labels. In this paper, we discuss an algorithm for finding the sparin"},"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":"1512.01113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-12-02T10:53:08Z","cross_cats_sorted":[],"title_canon_sha256":"ec1c976a2cf7b74733b519856759972955927a752ca4d6eca5acf10176ad6637","abstract_canon_sha256":"c33266669d863cf789b3ee9d7cf706b6160a80657262dd36be8ee758a7ecc600"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:18.925487Z","signature_b64":"xByZa6e4SXPFpJrUFTSqvNvVcZCh8wPTGMm5uBd907jFr6Cqj8zQlLT4IV4ATT0eMvJG3teLYxbEk7to8dIqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd9ef3b8942a5769f5d897b5ba5cd7359d6fd825efe28ae57ad173b6abb8bd20","last_reissued_at":"2026-05-18T01:25:18.924815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:18.924815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Sparing Number Algorithm of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"K. 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