Skip to main content
Log in

Arc-transitive cubic cayley graphs on PSL(2, p)

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

For a prime p at least 5, let T = PSL(2, p). This paper gives a classification of the connected arc-transitive cubic Cayley graphs on T and a determination of the generated pairs (ā,−) of T such that o(ā) = 2 and o(−)= 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. Biggs, N. L., Algebraic Graph Theory, Cambridge: Cambridge University Press, 1974.

    MATH  Google Scholar 

  2. Huppert, B., Endliche Gruppen I, Berlin: Springer-Verlag, 1967.

    MATH  Google Scholar 

  3. Tutte, W. T., A family of cubic graphs, Proc. Cambr. Philosoph. Soc., 1947, 43: 459–474.

    Article  MATH  MathSciNet  Google Scholar 

  4. Tutte, W. T., On the symmetry of cubic graphs, Can. J. Math. 1959, 11: 621–624.

    MATH  MathSciNet  Google Scholar 

  5. Conder, M. D. E., Lorimer, P., Automorphism groups of symmetric graphs of valency 3, J. Combin. Theory (B), 1989, 47: 60–72.

    Article  MATH  MathSciNet  Google Scholar 

  6. Conder, M. D. E., Praeger, C. E., Remarks on path-transitivity on finite graphs, Europ. J. Combin., 1996, 17: 371–378.

    Article  MATH  MathSciNet  Google Scholar 

  7. Djoković, D. Ž., Miller, G. L., Regular groups of automorphisms of cubic graphs, J. Combin. Theory (B), 1980, 29: 195–230.

    Article  MATH  Google Scholar 

  8. Frucht, R., A one-regular graph of degree three, Canad. J. Math., 1952, 4: 240–247.

    MATH  MathSciNet  Google Scholar 

  9. Gosil, C. D., The automorphism groups of some cubic Cayley graphs, Europ. J. Combin., 1983, 4: 25–32.

    Google Scholar 

  10. Miller, R. C., The trivalent symmetric graphs of girth at most six, J. Combin. Theory (B), 1971, 10: 163–182.

    Article  MATH  Google Scholar 

  11. Marušič, D., Pisanski, P., Symmetries of hexagonal molecular graphs on the torus, Croat. Chemica Acta., 2000, 72: 69–82.

    Google Scholar 

  12. Fang, X. G., Li, C. H., Wang, J. et al., On cubic normal Cayley graphs of finite simple groups, Discrete Math., 2002, 244: 67–75.

    Article  MATH  MathSciNet  Google Scholar 

  13. Xu, S. J., Fang, X. G., Wang, J. et al., On cubic s-arc-transtive Cayley graphs of finite simple groups, Euro J. of Combin., 2005, 26: 133–143.

    Article  MATH  MathSciNet  Google Scholar 

  14. Xu, M. Y., Xu, S. J., The symmetry properties of Cayley graphs of small valencies on the alternating group A 5, Sci. China, Ser. A, 2004, 47: 593–604.

    Article  MATH  MathSciNet  Google Scholar 

  15. Xu, M. Y., Automorphism groups and isomorphisms of Cayley digraphs, Discrete Math., 1998, 182: 309–319.

    Article  MATH  MathSciNet  Google Scholar 

  16. Dickson, L. E., Linear Groups with an exposition of the Galois field theory, Leipzig, 1901; Dover Publ. 1958.

    MATH  Google Scholar 

  17. Pan, C. D., Pan, C. B., Elementary Number Theory (in Chinese), Beijing: Beijing University Press, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Du Shaofei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Du, S., Wang, F. Arc-transitive cubic cayley graphs on PSL(2, p). Sci. China Ser. A-Math. 48, 1297–1308 (2005). https://doi.org/10.1360/03ys0374

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1360/03ys0374

Keywords

Navigation