International Journal of Nonlinear Analysis and Applications

Perfect 2-coloring of the six regular graphs up to order 10

Document Type : Research Paper

Authors

School of Mathematics and Computer Science, Iran University of Science and Technology, Tehran , Iran.

Abstract

In this paper, we study perfect 2-coloring of the six-regular graphs up to order 10. We first obtain all possible color parameter matrices and then examine them according to the limitation of our theorem.

Keywords

[1] M. Alaeiyan and H. Karami, Perfect 2-colorings of the generalized Petersen graph, Proc. Math. Sci. 126 (2016), 289–294.
[2] M. Alaeiyan and A. Mehrabani, Perfect 3-colorings of the cubic graphs of order 10, Electron. J. Graph Theory Appl. 5 (2017), no. 2, 194–206.
[3] M. Alaiyan and A. Mehrabani, Perfect 3-colorings of the platonic graph, Iranian J. Sci. Technol.: Trans. A Sci. 43 (2019), 1863–1871.
[4] M. Alaiyan and A. Mehrabani, Perfect 3-colorings of cubic graphs of order 8, Armen. J. Math. 10 (2018), no. 2, 1–9.
[5] M. Alaeiyan and A. Mehrabani, Perfect 2-colorings of the cubic graphs of order less than or equal to 10, AKCE Int. J. Graphs Combin. 17 (2020), no. 1, 380–386.
[6] 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, Springer, 2008.
[7] D. G. Fon-Der-Flaass, Perfect 2-colorings of a hypercube, Sib. Math. J. 4 (2007), 923–930.
[8] D. G. Fon-der Flaass, Perfect 2-colorings of a 12-dimensional cube that achieve a bound of correlation immunity, Sib. Math. J. 4 (2007), 292–295.
[9] A. L. Gavrilyuk and S.V. Goryainov, On perfect 2-colorings of Johnson graphs J(v,3), J. Combin. Des. 21 (2013), 232–252.
[10] F.C. Bussemaker, S. Cobeljic, D.M. Cvetkovic, and J.J. Seidel, Computer Investigation of Cubic Graphs, Tech. Hogeschool Eindhoven Ned. Onderafedeling Wisk, 1976.
International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 3
March 2025
Pages 19-25
  • Receive Date: 05 July 2023
  • Accept Date: 24 October 2023