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Antibandwidth and cyclic antibandwidth of Hamming graphs
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 bound...
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Published in: | Discrete Applied Mathematics 2013-07, Vol.161 (10-11), p.1402-1408 |
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container_title | Discrete Applied Mathematics |
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creator | Dobrev, Stefan Královič, Rastislav Pardubská, Dana Török, L’ubomír Vrt’o, Imrich |
description | 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 Πk=1dKnk. We have exact values for special choices of ni′s and equality between antibandwidth and cyclic antibandwidth values. Moreover, in the case where the two largest sizes of ni′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. |
doi_str_mv | 10.1016/j.dam.2012.12.026 |
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subjects | Algorithms Antibandwidth Graphs Hamming graph Integers Labels Marking Mathematical analysis Reproduction Upper bounds |
title | Antibandwidth and cyclic antibandwidth of Hamming graphs |
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