Skip to main content
Log in

Perfect 2-colorings of the generalized Petersen graph

  • Published:
Proceedings - Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we enumerate the parameter matrices of all perfect 2-colorings of the generalized Petersen graphs GP (n,2), where n ≥ 5. We also present some basic results for GP (n, k), where n ≥ 5 and k ≥ 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. Avgustinovich S V and Mogilnykh I Yu, Perfect 2-colorings of Johnson graphs J(6, 3) and J(7, 3), Lect. Notes Comput. Sci. 5228 (2008) 11–19

    Article  MATH  Google Scholar 

  2. Avgustinovich S V and Mogilnykh I Yu, Perfect colorings of the Johnson graphs J(8, 3) and J(8, 4) with two colors, J. Appl. Industrial Math. 5 (2011) 19–30

    Article  MATH  Google Scholar 

  3. Fon-Der-Flaass D G, A bound on correlation immunity, Sib. Electron. Math. Reports J. 4 (2007) 133–135

    MathSciNet  MATH  Google Scholar 

  4. Fon-Der-Flaass D G, Perfect 2-colorings of a hypercube, Sib. Math. J. 4 (2007) 923–930

    MathSciNet  MATH  Google Scholar 

  5. Fon-Der-Flaass D G, Perfect 2-colorings of a 12-dimensional cube that achieve a bound of correlation immunity, Sib. Math. J. 4 (2007) 292–295

    MathSciNet  MATH  Google Scholar 

  6. Gavrilyuk A L and Goryainov S V, On perfect 2-colorings of Johnson graphs J(v, 3), J. Comb. Des. 21 (2013) 232–252

    Article  MathSciNet  MATH  Google Scholar 

  7. Godsil C, Compact graphs and equitable partitions, Linear Algebra Appl. 255 (1997) 259–266

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to HAMED KARAMI.

Additional information

Communicating Editor: Parameswaran Sankaran

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

ALAEIYAN, M., KARAMI, H. Perfect 2-colorings of the generalized Petersen graph. Proc Math Sci 126, 289–294 (2016). https://doi.org/10.1007/s12044-016-0285-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12044-016-0285-4

Keywords

2010 Mathematics Subject Classification.

Navigation