Associativity and Non-Associativity of Some Hypergraph Products

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. R. H. Hammack Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA e-mail: [email protected] M. Hellmuth (B) Department of Mathematics and Computer Science, University of Greifswald, Walther-Rathenau-Straße 47, 17487 Greifswald, Germany e-mail: [email protected] M. Hellmuth Center for Bioinformatics, Saarland University, Building E 2.1, Room 413, P.O. Box 15 11 50, 66041 Saarbrücken, Germany L. Ostermeier · P. F. Stadler Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for Bioinformatics, University of Leipzig, Härtelstraße 16-18, 04107 Leipzig, Germany e-mail: [email protected] P. F. Stadler e-mail: [email protected] P. F. Stadler Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany P. F. Stadler RNomics Group, Fraunhofer Institut für Zelltherapie und Immunologie, Deutscher Platz 5e, 04103 Leipzig, Germany P. F. Stadler Department of Theoretical Chemistry, University of Vienna, Währingerstraße 17, 1090 Vienna, Austria P. F. Stadler Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA R. H. Hammack et al.