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Associativity and Non-Associativity of Some Hypergraph Products

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Abstract

Several variants of hypergraph products have been introduced as generalizations of the strong and direct products of graphs. Here we show that only some of them are associative. In addition to the Cartesian product, these are the minimal rank preserving direct product, and the normal product. Counter-examples are given for the strong product as well as the non-rank-preserving and the maximal rank preserving direct product.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, 23284-2014, USA

    Richard H. Hammack

  2. Department of Mathematics and Computer Science, University of Greifswald, Walther-Rathenau-Straße 47, 17487, Greifswald, Germany

    Marc Hellmuth

  3. Center for Bioinformatics, Saarland University, Building E 2.1, Room 413, P.O. Box 15 11 50, 66041, Saarbrücken, Germany

    Marc Hellmuth

  4. Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for Bioinformatics, University of Leipzig, Härtelstraße 16-18, 04107, Leipzig, Germany

    Lydia Ostermeier & Peter F. Stadler

  5. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany

    Peter F. Stadler

  6. RNomics Group, Fraunhofer Institut für Zelltherapie und Immunologie, Deutscher Platz 5e, 04103, Leipzig, Germany

    Peter F. Stadler

  7. Department of Theoretical Chemistry, University of Vienna, Währingerstraße 17, 1090, Vienna, Austria

    Peter F. Stadler

  8. Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM, 87501, USA

    Peter F. Stadler

Authors
  1. Richard H. Hammack
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  2. Marc Hellmuth
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  3. Lydia Ostermeier
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  4. Peter F. Stadler
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Correspondence to Marc Hellmuth.

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Hammack, R.H., Hellmuth, M., Ostermeier, L. et al. Associativity and Non-Associativity of Some Hypergraph Products. Math.Comput.Sci. 10, 403–408 (2016). https://doi.org/10.1007/s11786-016-0276-y

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  • DOI: https://doi.org/10.1007/s11786-016-0276-y

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