{"paper":{"title":"A Study on Integer Additive Set-Graceful Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"K. A. Germina, N. K. Sudev","submitted_at":"2014-03-17T01:59:43Z","abstract_excerpt":"A set-labeling of a graph $G$ is an injective function $f:V(G)\\to \\mathcal{P}(X)$, where $X$ is a finite set and a set-indexer of $G$ is a set-labeling such that the induced function $f^{\\oplus}:E(G)\\rightarrow \\mathcal{P}(X)-\\{\\emptyset\\}$ defined by $f^{\\oplus}(uv) = f(u){\\oplus}f(v)$ for every $uv{\\in} E(G)$ is also injective. An integer additive set-labeling is an injective function $f:V(G)\\rightarrow \\mathcal{P}(\\mathbb{N}_0)$, $\\mathbb{N}_0$ is the set of all non-negative integers and an integer additive set-indexer is an integer additive set-labeling such that the induced function $f^+:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3984","kind":"arxiv","version":3},"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"}