Cube-magic labelings of grids

Original · EN

We show that the vertices and edges of a d-dimensional grid graph G=(V,E) (d 2) can be labeled with the integers from {1,, V} and {1,, E}, respectively, in such a way that for every subgraph H isomorphic to a d-cube the sum of all the labels of H is the same. As a consequence, for every d 2, every d-dimensional grid graph is Qd-supermagic where Qd is the d-cube.