Antibandwidth and cyclic antibandwidth of Hamming graphs

  • Authors:

  • Stefan Dobrev;Rastislav KráLovič;Dana Pardubská;L'UbomíR TöRöK;Imrich Vrt'O

  • Affiliations:

  • Institute of Mathematics, Slovak Academy of Sciences, Dúbravská 9, 841 04 Bratislava, Slovakia;Department of Computer Science, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia;Department of Computer Science, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia;Institute of Mathematics and Computer Science, Slovak Academy of Sciences and Matej Bel University, umbierska 1, 974 11, Banská Bystrica, Slovakia;Institute of Mathematics, Slovak Academy of Sciences, Dúbravská 9, 841 04 Bratislava, Slovakia

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2013

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Abstract

The antibandwidth problem is to label vertices of a 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 maximized. In this paper we study the antibandwidth of Hamming graphs. We provide labeling algorithms and tight upper bounds for general Hamming graphs @P"k"="1^dK"n"""k. We have exact values for special choices of n"i^'s and equality between antibandwidth and cyclic antibandwidth values. Moreover, in the case where the two largest sizes of n"i^'s are different we show that the Hamming graph is multiplicative in the sense of [9]. As a consequence, we obtain exact values for the antibandwidth of p isolated copies of this type of Hamming graphs.