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An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\mathscr{P}(X)-\\{\\emptyset\\}$ such that the induced function $f^+:E(G) \\to \\mathscr{P}(X)-\\{\\emptyset\\}$ is defined by $f^+(uv)=f(u)+f(v);\\ \\forall\\, uv\\in E(G)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. An IASL of a signed graph is an IASL of its underlying graph $G$ together with the signature $\\sigma$ defined by $\\sigma(uv)=(-1)^{|f^+(uv)|};\\ \\forall\\, uv\\in E(\\Sigma)$. In this paper, we discu"},"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":"1609.00295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-09-01T16:05:23Z","cross_cats_sorted":[],"title_canon_sha256":"bb08ffa3f8531bf427ac4fff19a09164d27c592ae55c0f7ebb4039ec8147d8ce","abstract_canon_sha256":"38fa5dceec42cb1ae549b34254158b89fb6397d2e98f5aaa5c2372431022ef43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:25.199276Z","signature_b64":"VFhbDoz1fSYD1VO0xFPOuVnq4GMyhGNFrDX9hc7aN8y6V62s5iHnOh6KxTZgYy0iI0BVOr/uWctFCDVJ/KLnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84a368dc97a78c007bbe4ef8a819cdb5add2c42edcc08777d96391883fa88558","last_reissued_at":"2026-05-18T01:06:25.198782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:25.198782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some New Results on Integer Additive Set-Valued Signed Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"K. A. Germina, N. K. Sudev, P. K. Ashraf","submitted_at":"2016-09-01T16:05:23Z","abstract_excerpt":"Let $X$ denotes a set of non-negative integers and $\\mathscr{P}(X)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\mathscr{P}(X)-\\{\\emptyset\\}$ such that the induced function $f^+:E(G) \\to \\mathscr{P}(X)-\\{\\emptyset\\}$ is defined by $f^+(uv)=f(u)+f(v);\\ \\forall\\, uv\\in E(G)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. An IASL of a signed graph is an IASL of its underlying graph $G$ together with the signature $\\sigma$ defined by $\\sigma(uv)=(-1)^{|f^+(uv)|};\\ \\forall\\, uv\\in E(\\Sigma)$. 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