{"paper":{"title":"Group distance magic graphs $G\\times C_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sylwia Cichacz","submitted_at":"2013-02-26T20:11:29Z","abstract_excerpt":"A $\\Gamma$-distance magic labeling of a graph $G=(V,E)$ with $|V | = n$ is a bijection $f$ from $V$ to an Abelian group $\\Gamma$ of order $n$ such that the weight $w(x)=\\sum_{y\\in N_G(x)}f(y)$ of every vertex $x \\in V$ is equal to the same element $\\mu \\in \\Gamma$, called the \\emph{magic constant}.\n  In this paper we will show that if $G$ is a graph of order $n=2^{p}(2k+1)$ for some natural numbers $p$, $k$ such that $\\deg(v)\\equiv c \\imod {2^{p+2}}$ for some constant $c$ for any $v\\in V(G)$, then there exists a $\\Gamma$-distance magic labeling for any Abelian group $\\Gamma$ of order $4n$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6561","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"}