Skip to main content
Log in

Spherical Embeddings of Symmetric Association Schemes in 3-Dimensional Euclidean Space

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with \(m_1 = 3\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bannai, E., Bannai, E.: On primitive symmetric association schemes with \(m_1=3\). Contrib. Discrete Math. 1(1), 68–79 (2006)

    MathSciNet  MATH  Google Scholar 

  2. Bannai, E., Bannai, E., Ito, T.: Introduction to Algebraic Combinatorics. Kyoritsu Shuppan, Tokyo (2016)

    MATH  Google Scholar 

  3. Bannai, E., Ito, T.: Algebraic Combinatorics. I. Association Schemes. The Benjamin/Cummings Publishing Co., Inc., Menlo Park (1984)

    MATH  Google Scholar 

  4. Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance-regular graphs. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 18. Springer, Berlin (1989). https://doi.org/10.1007/978-3-642-74341-2

  5. van Dam, E.R., Koolen, J.H., Park, J.: Partially metric association schemes with a multiplicity three. J. Comb. Theory Ser. B 130, 19–48 (2018). https://doi.org/10.1016/j.jctb.2017.09.011

    Article  MathSciNet  MATH  Google Scholar 

  6. Martin, W.J., Williford, J.S.: There are finitely many \(Q\)-polynomial association schemes with given first multiplicity at least three. Eur. J. Comb. 30(3), 698–704 (2009). https://doi.org/10.1016/j.ejc.2008.07.009

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported in part by NSFC Grant 11271257 and 11671258.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Da Zhao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bannai, E., Zhao, D. Spherical Embeddings of Symmetric Association Schemes in 3-Dimensional Euclidean Space. Graphs and Combinatorics 36, 245–250 (2020). https://doi.org/10.1007/s00373-019-02075-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-019-02075-6

Keywords

Mathematics Subject Classification

Navigation