Antibandwidth of Three-Dimensional Meshes

The antibandwidth problem is to label vertices of a graph G=(V,E) bijectively by 0,1,2,...,|V|-1 so that the minimal difference of labels of adjacent vertices is maximised. In this paper we prove an almost exact result for the antibandwidth of three-dimensional meshes. Provided results are extensions of the two-dimensional case and an analogue of the result for the bandwidth of three-dimensional meshes obtained by FitzGerald.

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