Skip to main content
SpringerLink
Log in

On automorphisms of a distance-regular graph with intersection array {204, 175, 48, 1; 1, 12, 175, 204}

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

A distance-regular graph Γ with intersection array {204, 175, 48, 1; 1, 12, 175, 204} is an AT4-graph, and the antipodal quotient \(\overline \Gamma \) has parameters (800, 204, 28, 60). Automorphisms of these graphs are found. In particular, neither of the two graphs is arc-transitive.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs (Springer, Berlin, 1989).

    Book  MATH  Google Scholar 

  2. A. A. Makhnev and D. V. Paduchikh, “On strongly regular graphs with eigenvalue µ and their extensions,” Tr. Inst. Mat. Mekh. 19 (3), 207–214 (2013).

    Google Scholar 

  3. A. A. Makhnev and D. V. Paduchikh, “On automorphisms of strongly regular graphs with parameters (204,28,2,4) and (595,144,18,40),” in Discrete Mathematics, Algebra, and Applications: Abstracts of the International Conference, Minsk, Belarus, 2015, pp. 119–120.

    Google Scholar 

  4. P. J. Cameron, Permutation Groups (Cambridge Univ. Press, Cambridge, 1999), Ser. London Mathematical Society Student Texts 45.

    Book  MATH  Google Scholar 

  5. A. E. Brouwer and W. H. Haemers, “The Gewirtz graph: An exercise in the theory of graph spectra,” Europ. J. Comb. 14, 397–407 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. L. Gavrilyuk and A. A. Makhnev, “On automorphisms of distance-regular graphs with intersection array {56, 45, 1; 1, 9, 56},” Dokl. Math. 81 (3), 439–442 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. V. Zavarnitsine, “Finite simple groups with narrow prime spectrum,” Sib. Elektron. Mat. Izv. 6, 1–12 (2009).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    A. A. Makhnev, M. S. Nirova & D. V. Paduchikh

  2. Ural Federal University, Yekaterinburg, 620002, Russia

    A. A. Makhnev

  3. Kabardino-Balkar State University, Nalchik, 360004, Kabardino-Balkar Republic, Russia

    M. S. Nirova

Authors
  1. A. A. Makhnev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. Nirova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. V. Paduchikh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Makhnev.

Additional information

Original Russian Text © A.A.Makhnev, M.S. Nirova, D.V. Paduchikh, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 1.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Makhnev, A.A., Nirova, M.S. & Paduchikh, D.V. On automorphisms of a distance-regular graph with intersection array {204, 175, 48, 1; 1, 12, 175, 204}. Proc. Steklov Inst. Math. 295 (Suppl 1), 101–108 (2016). https://doi.org/10.1134/S008154381609011X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S008154381609011X

Keywords

Search

Navigation