Antibandwidth of three-dimensional meshes

The antibandwidth problem is to label vertices of a graph G=(V,E)G=(V,E) bijectively by 0,1,2,…,|V|−10,1,2,…,|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.