{"paper":{"title":"A Study on Arithmetic Integer Additive Set-Indexers of 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":"2013-12-30T10:50:12Z","abstract_excerpt":"A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \\rightarrow2^{X}$ such that the function $f^{\\oplus}:E(G)\\rightarrow2^{X}-\\{\\emptyset\\}$ defined by $f^{\\oplus}(uv) = f(u){\\oplus} f(v)$ for every $uv{\\in} E(G)$ is also injective, where $2^{X}$ is the set of all subsets of $X$ and $\\oplus$ is the symmetric difference of sets. An integer additive set-indexer is defined as an injective function $f:V(G)\\rightarrow 2^{\\mathbb{N}_0}$ such that the induced function $f^+:E(G) \\rightarrow 2^{\\mathbb{N}_0}$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. A graph $G$ which a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7674","kind":"arxiv","version":5},"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"}