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Group distance magic labeling of Cartesian product of cycles. (English) Zbl 1278.05210
Summary: A group distance magic labeling of a graph \(G(V,E)\) with \(|V|=n\) is an injection from \(V\) to an abelian group \(\Gamma\) of order \(n\) such that the sum of labels of all neighbors of every vertex \(x\in V\) is equal to the same element \(\mu\in\Gamma\). We completely characterize all Cartesian products \(C_k\square C_m\) that admit a group distance magic labeling by \(Z_{km}\).

MSC:
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C76 Graph operations (line graphs, products, etc.)
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