On group-magic graphs (Q2747195)

Given an abelian group \(A\), a graph \(G=(V,E)\) is \(A\)-magic if there exists a labeling \(\ell\) of the edges with elements from \(A - \{0\}\) such that the induced vertex labeling \(\ell^\ast\) with \(\ell^\ast(v) = \sum \{\ell(u,v)\mid \{u,v\}\in E\}\) is a constant map. This paper gives several results on whether specific types of graphs are \(A\)-magic for abelian groups \(A\); sometimes specifically for \(A=Z_k\).