Antibandwidth of three-dimensional meshes

Abstract

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. © 2009 Elsevier B.V. All rights reserved.