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Unification of Graph Products and Compatibility with Switching

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Abstract

We define the type of graph products, which enable us to treat many graph products in a unified manner. These unified graph products are shown to be compatible with Godsil–McKay switching. Furthermore, by this compatibility, we show that the Doob graphs can also be obtained from the Hamming graphs by switching.

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Acknowledgements

The author would like to thank Akihiro Munemasa for helpful advice and Tomonori Hashikawa for valuable comments on Sect. 5.2.

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  1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Sho Kubota

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  1. Sho Kubota
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Correspondence to Sho Kubota.

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Kubota, S. Unification of Graph Products and Compatibility with Switching. Graphs and Combinatorics 33, 1347–1355 (2017). https://doi.org/10.1007/s00373-017-1848-6

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  • DOI: https://doi.org/10.1007/s00373-017-1848-6

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