# zbMATH — the first resource for mathematics

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.)
Full Text: