{"paper":{"title":"On Weak Integer Additive Set-Indexers of Certain Graph Classes","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":"2014-02-27T18:58:58Z","abstract_excerpt":"An integer additive set-indexer is defined as an injective function $f:V(G)\\rightarrow 2^{\\mathbb{N}_0}$ such that the induced function $g_f:E(G) \\rightarrow 2^{\\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. An integer additive set-indexer is said to be $k$-uniform if $|g_f(uv)|=k$ for all $u,v\\in V(G)$. An integer additive set-indexer $f$ is said to be a weak IASI if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\\in V(G)$. The sparing number of a graph $G$ is the minimum number of edges in $G$ with singleton set-labels, so that $G$ admits a weak integer additive set-indexer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7020","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"}