{"paper":{"title":"The inapproximability for the (0,1)-additive number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.CO","authors_text":"Ali Dehghan, Arash Ahadi","submitted_at":"2013-06-02T07:56:50Z","abstract_excerpt":"An\n  {\\it additive labeling} of a graph $G$ is a function $ \\ell :V(G) \\rightarrow\\mathbb{N}$, such that for every two adjacent vertices $ v $ and $ u$ of $ G $, $ \\sum_{w \\sim v}\\ell(w)\\neq \\sum_{w \\sim u}\\ell(w) $ ($ x \\sim y $ means that $ x $ is joined to $y$). The {\\it additive number} of $ G $, denoted by $\\eta(G)$, is the minimum number $k $ such that $ G $ has a additive labeling $ \\ell :V(G) \\rightarrow \\mathbb{N}_k$. The {\\it additive choosability} of a graph $G$, denoted by $\\eta_{\\ell}(G) $, is the smallest number $k$ such that $G$ has an additive labeling for any assignment of lis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0182","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"}