{"paper":{"title":"Group Irregular Labelings of Disconnected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcin Anholcer, Sylwia Cichacz","submitted_at":"2012-09-02T18:20:28Z","abstract_excerpt":"We investigate the \\textit{group irregularity strength} ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\\gr$ of order $s$, there exists a function $f:E(G)\\rightarrow \\gr$ such that the sums of edge labels at every vertex are distinct. We give the exact values and bounds on $s_g(G)$ for chosen families of disconnected graphs. In addition we present some results for the \\textit{modular edge gracefulness} $k(G)$, i.e. the smallest value of $s$ such that there exists a function $f:E(G)\\rightarrow \\zet_s$ such that the sums of edge labels at every vertex are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0200","kind":"arxiv","version":1},"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"}