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Mutually Orthogonal Sudoku Latin Squares and Their Graphs

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Abstract

We introduce a graph attached to mutually orthogonal Sudoku Latin squares. The spectra of the graphs obtained from finite fields are explicitly determined. As a corollary, we then use the eigenvalues to distinguish non-isomorphic Sudoku Latin squares.

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Acknowledgements

The authors would like to thank the referees for their careful reading and valuable comments. Sho Kubota is supported by JSPS KAKENHI Grant Number 20J01175, and Sho Suda is supported by JSPS KAKENHI Grant Number 18K03395 and 22K03410.

Funding

JSPS 20J01175, 18K03395.

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Authors and Affiliations

  1. Faculty of Information Science and Technology, Faculty of Engineering, Osaka Institute of Technology, Hirakata, Osaka, 573-0196, Japan

    Sho Kubota

  2. Department of Mathematics, National Defense Academy of Japan, Yokosuka, Kanagawa, 239-8686, Japan

    Sho Suda

  3. Shanghai Japanese School Pudong Campus, Shanghai, 201204, China

    Akane Urano

Authors
  1. Sho Kubota
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  2. Sho Suda
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  3. Akane Urano
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Correspondence to Sho Kubota.

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Kubota, S., Suda, S. & Urano, A. Mutually Orthogonal Sudoku Latin Squares and Their Graphs. Graphs and Combinatorics 39, 122 (2023). https://doi.org/10.1007/s00373-023-02718-9

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  • DOI: https://doi.org/10.1007/s00373-023-02718-9

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