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Perfect 2-coloring of the six regular graphs up to order 10 | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 16، شماره 3، خرداد 2025، صفحه 19-25 اصل مقاله (362.38 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31154.4576 | ||
| نویسندگان | ||
| Mozhgan Keyhani؛ Mehdi Alaeiyan* | ||
| School of Mathematics and Computer Science, Iran University of Science and Technology, Tehran , Iran. | ||
| تاریخ دریافت: 14 تیر 1402، تاریخ پذیرش: 02 آبان 1402 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Regular graph؛ Parameter matrices؛ Perfect coloring | ||
| مراجع | ||
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[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. | ||
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