Perfect 2-colorings of the generalized Petersen graph GP(n,3)

Hamed Karami


In this paper we enumerate the parameter matrices of all perfect 2-colorings of the generalized Petersen graphs GP(n, 3), where n ≥ 7. We also give some basic results for GP(n, k).


Perfect Coloring; Equitable Partition; Generalized Petersen graphs

Full Text:




A. Mehdi and K. Hamed, Perfect 2-colorings of generalized Petersen graphs, Proc. Indian Acad. Sci. 126 (3) (2016), 289–294.

A. Mehdi, K. Hamed, and S. Sajjad, Perfect 3-colorings of GP(5, 2), GP(6, 2), and GP(7, 2), Journal of the Indonesian Mathematical Society 24 (2) 2018, 47–53.

A.M. Hadi and K. Hamed, Perfect 2-colorings of Platonic graphs, Proc. Iranian Journal of Nonlinear Analysis and Application 8 (2) (2017), 29–35.

S.V. Avgustinovich and I. Yu. Mogilnykh, Perfect 2-colorings of Johnson graphs J(6, 3) and J(7, 3), Lecture Notes in Computer Science 5228 (2008), 11–19.

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

D.G. Fon-Der-Flaass, A bound on correlation immunity, Siberian Electronic Mathematical Reports Journal 4 (2007), 133–135.

D.G. Fon-Der-Flaass, Perfect 2-colorings of a hypercube, Siberian Mathematical Journal, 4 (2007), 923–930.

D.G. Fon-der-Flaass, Perfect 2-colorings of a 12-dimensional Cube that achieve a bound of correlation immunity, Siberian Mathematical Journal 4 (2007), 292–295.

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

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


  • There are currently no refbacks.

ISSN: 2338-2287

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View EJGTA Stats