Antibandwidth and Cyclic Antibandwidth of Hamming Graphs

The antibandwidth problem is to label vertices of graph G ( V , E ) bijectively by integers 0 , 1 , … , | V | − 1 in such a way that the minimal difference of labels of adjacent vertices is maximised. In this paper we study the antibandwidth of Hamming graphs. We provide labeling algorithms and tight upper bounds for general Hamming graphs ∏ k = 1 d K n k . We have exact values for special choices of n i ʹs and equality between antibandwidth and cyclic antibandwidth values.