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Switching graphs and Hadamard matrices

Дата публикации: 21-05-2026 00:00:00

Local operations of combinatorial structures (graphs, Hadamard matrices, codes, designs) that maintain the basic parameters unaltered, have been widely used in the literature under the name of switching. We show an equivalence between two switching methods to construct inequivalent Hadamard matrices, which were proposed by Orrick in 2008, and the switching method for constructing cospectral graphs which was introduced by Godsil and McKay in 1982.

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Authors
  • Aida Abiad Eindhoven University of Technology, Netherlands and Vrije Universiteit Brussel, Belgium
  • Louka Peters Ghent University, Belgium
DOI: https://doi.org/10.26493/2590-9770.1840.c3u Keywords: Switching, cospectral graph, Hadamard matrix Abstract

Local operations of combinatorial structures (graphs, Hadamard matrices, codes, designs) that maintain the basic parameters unaltered, have been widely used in the literature under the name of switching. We show an equivalence between two switching methods to construct inequivalent Hadamard matrices, which were proposed by Orrick in 2008, and the switching method for constructing cospectral graphs which was introduced by Godsil and McKay in 1982.

Issue Section

Open Problems on Rank Metric Codes

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