Skip to main content
SpringerLink
Log in

On the Non-Existence of \(\mathrm{{srg}(76,21,2,7)}\)

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

Abstract

We present a new non-existence proof for the strongly regular graph G with parameters (76, 21, 2, 7), using the unit vector representation of the graph.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Similar content being viewed by others

Notes

  1. We thank the referee for pointing this out to us.

References

  1. Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Universitext. Springer, New York (2012)

    Book  MATH  Google Scholar 

  2. Dixmier, S., Zara, F.: Etude d’un quadrangle généralisé author de deux de ses point non liés (1976) (unpublished manuscript)

  3. Godsil, C.D.: Algebraic Combinatorics. Chapman & Hall, New York (1993)

    MATH  Google Scholar 

  4. Haemers, W.H.: There exists no (76, 21, 2, 7) strongly regular graph. In: de Clerck, F., Beutelspacher, A. (eds.) Finite Geometry and Combinatorics: The Second International Conference at Deinze, London Mathematical Society Lecture Notes Series, pp. 175–176. Cambridge University Press, Cambridge (1993)

    Chapter  Google Scholar 

  5. Humphreys, J.E.: Reflection Groups and Coxeter Groups. Cambridge University Press, Cambridge (1990)

    Book  MATH  Google Scholar 

  6. van Lint, J.H., Brouwer, A.E.: Strongly regular graphs and partial geometries. In: Jackson, D.H., Vanstone, S.A. (eds.) Enumeration and Design, pp. 85–122. Academic Press, New York (1984)

    Google Scholar 

Download references

Acknowledgements

The authors are grateful to King Fahd University of Petroleum and Minerals for supporting this research.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Monther R. Alfuraidan & Ibrahim O. Sarumi

  2. School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    Sergey Shpectorov

Authors
  1. Monther R. Alfuraidan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ibrahim O. Sarumi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergey Shpectorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergey Shpectorov.

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

Alfuraidan, M.R., Sarumi, I.O. & Shpectorov, S. On the Non-Existence of \(\mathrm{{srg}(76,21,2,7)}\). Graphs and Combinatorics 35, 847–854 (2019). https://doi.org/10.1007/s00373-019-02039-w

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-019-02039-w

Keywords

Mathematics Subject Classification

Search

Navigation