Antibandwidth of Three-Dimensional Meshes

The antibandwidth problem is to label vertices of a graph G=(V,E) bijectively by 1,2,3,…,|V| such that the minimal difference of labels of adjacent vertices is maximised. In this paper we discuss the antibandwidth of three-dimensional meshes. Provided results are extensions of the two-dimensional case and an analog of the result for the bandwidth of three-dimensional meshes obtained by FitzGerald.