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.