{"paper":{"title":"Group Irregularity Strength of Connected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcin Anholcer, Martin Milanic, Sylwia Cichacz","submitted_at":"2012-05-11T16:42:33Z","abstract_excerpt":"We investigate the 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 prove that for any connected graph $G$ of order at least 3, $s_g(G)=n$ if $n\\neq 4k+2$ and $s_g(G)\\leq n+1$ otherwise, except the case of some infinite family of stars."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2569","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"}