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Recognizing binary Hamming graphs inO(n 2 logn) time

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Abstract

A graphG is called a binary Hamming graph if each vertex ofG can be assigned a binary address of fixed length such that the Hamming distance between two addresses equals the length of a shortest path between the corresponding vertices. It is shown thatO(n 2 logn) time suffices for deciding whether a givenn-vertex graphG is a binary Hamming graph, and for computing a valid addressing scheme forG provided it exists. This is not far from being optimal asn addresses of lengthn — 1 have to be computed in the worst case.

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Authors and Affiliations

  1. Institute für Informationsverarbeitung, Technische Universität Graz, Graz, Austria

    F. Aurenhammer & J. Hagauer

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  1. F. Aurenhammer
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  2. J. Hagauer
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Aurenhammer, F., Hagauer, J. Recognizing binary Hamming graphs inO(n 2 logn) time. Math. Systems Theory 28, 387–395 (1995). https://doi.org/10.1007/BF01185863

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  • DOI: https://doi.org/10.1007/BF01185863

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