Skip to main content
Log in

Edge-Symmetric Distance-Regular Coverings of Complete Graphs: the Almost Simple Case

  • Published:
Algebra and Logic Aims and scope

We complete the classification of edge-symmetric distance-regular coverings of complete graphs with r /∉ {2, k, (k − 1)/μ} for the case of the almost simple action of an automorphism group of a graph on a set of its antipodal classes; here r is the order of an antipodal class.

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. A. A. Makhnev, D. V. Paduchikh, and L. Yu. Tsiovkina, “Arc-transitive distance-regular coverings of cliques with ⋋ = μ,” Trudy Inst. Mat. Mekh. UrO RAN, 19, No. 2, 237-246 (2013).

    Google Scholar 

  2. L. Yu. Tsiovkina, “Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with ⋋ = μ related to groups Sz(q) and 2 G 2(q),” J. Algebr. Comb., 41, No. 4, 1079-1087 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  3. L. Yu. Tsiovkina, “Arc-transitive antipodal distance-regular covers of complete graphs related to SU 3(q),” Discr. Math., 340, No. 2, 63-71 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. A. Makhnev, D. V. Paduchikh, and L. Yu. Tsiovkina, “Edge-symmetric distance-regular coverings of cliques: The affine case,” Sib. Math. J., 54, No. 6, 1076-1087 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  5. L. Yu. Tsiovkina, “On affine distance-regular covers of complete graphs,” Sib. El. Mat. Izv., 12, 998-1005 (2015); http://semr.math.nsc.ru/v12/p998-1005.pdf.

    MathSciNet  MATH  Google Scholar 

  6. C. D. Godsil, R. A. Liebler, and C. E. Praeger, “Antipodal distance transitive covers of complete graphs,” Eur. J. Comb., 19, No. 4, 455-478 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  7. C. D. Godsil, “Krein covers of complete graphs,” Australas. J. Comb., 6, 245-255 (1992).

    MathSciNet  MATH  Google Scholar 

  8. A. L. Gavrilyuk and A. A. Makhnev, “Geodesic graphs with homogeneity conditions,” Dokl. RAN, 422, No. 5, 589-591 (2008).

    MathSciNet  MATH  Google Scholar 

  9. V. D. Mazurov, “Minimal permutation representations of finite simple classical groups. Special linear, symplectic, and unitary groups,” Algebra and Logic, 32, No. 3, 142-153 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  10. V. D. Mazurov, “Minimal permutation representation of Thompson’s simple group,” Algebra and Logic, 27, No. 5, 350-361 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. V. Vasil’ev, “Minimal permutation representations of finite simple exceptional twisted groups,” Algebra and Logic, 37, No. 1, 9-20 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. V. Vasil’ev and V. D. Mazurov, “Minimal permutation representations of finite simple orthogonal groups,” Algebra and Logic, 33, No. 6, 337-350 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Guo, A. A. Makhnev, and D. V. Paduchikh, “On almost distance-transitive graphs,” Dokl. Akad. Nauk, 452, No. 6, 599-603 (2013).

    MathSciNet  MATH  Google Scholar 

  14. The GAP Group, GAP—Groups, Algorithms, Programming—A System for Computational Discrete Algebra, vers. 4.8.7 (2017); http://www.gap-system.org.

  15. P. J. Cameron, “Covers of graphs and EGQs,” Discr. Math., 97, Nos. 1-3, 83-92 (1991).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Makhnev.

Additional information

Translated from Algebra i Logika, Vol. 57, No. 2, pp. 214-231, March-April, 2018.

A. A. Makhnev, D. V. Paduchikh and L. Yu. Tsiovkina Supported by Russian Science Foundation, project 14-11-00061-P.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Makhnev, A.A., Paduchikh, D.V. & Tsiovkina, L.Y. Edge-Symmetric Distance-Regular Coverings of Complete Graphs: the Almost Simple Case. Algebra Logic 57, 141–152 (2018). https://doi.org/10.1007/s10469-018-9486-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-018-9486-5

Keywords

Navigation