{"paper":{"title":"A Creative Review on Integer Additive Set-Valued 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":"2014-07-27T10:35:00Z","abstract_excerpt":"For a non-empty ground set $X$, finite or infinite, the {\\em set-valuation} or {\\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \\to \\mathcal{P}(X)$, where $\\mathcal{P}(X)$ is the power set of the set $X$. A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \\to \\mathcal{P}(X)$ such that the function $f^{\\ast}:E(G)\\to \\mathcal{P}(X)-\\{\\emptyset\\}$ defined by $f^{\\ast}(uv) = f(u){\\ast} f(v)$ for every $uv{\\in} E(G)$ is also injective, where $\\ast$ is a binary operation on sets. An integer additive set-indexer is defined as an injective function $f:V(G)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7208","kind":"arxiv","version":2},"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"}