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Perfect 2-Colorings of Cn × Cm | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 1، شهریور 2023، صفحه 55-63 اصل مقاله (370.92 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2023.18779.1250 | ||
| نویسندگان | ||
| M. Alaeiyan* 1؛ M. Kamran Jamil2؛ MH. Alaeiyan3 | ||
| 1Department of Mathematics, Iran University of Science and Technology, Tehran, Iran | ||
| 2Department of Mathematic, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, 14 Ali Road, Lahore, Pakistan | ||
| 3Faculty of Computer Engineering, K. N. Toosi University of Technology, Seyed Khandan, , Tehran, Iran. | ||
| چکیده | ||
| In this paper, we enumerate the parameter matrices of all perfect 2-colorings of the generalized prism graph Cn × C3, where n ≥ 3,. We also present some generalized results for Cn × Cm, where m, n ≥ 3. | ||
| کلیدواژه‌ها | ||
| perfect colorings؛ equitable partition؛ generalized prism graph | ||
| مراجع | ||
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1. M. Alaeiyan, H. Karami, Perfect 2-coloring of the generalized Petersen graph, Proc. Indian Acad. Sci., (3) 126 (2016) 289-294. 2. M.H. Alaeiyan, H. Karami, Perfect 2-coloring of the Platonic graphs, Int. J. Nonlinear Anal. Appl., (2) 8 (2017) 29-35. 3. M. Alaeiyan, A. Abedi, M.H. Alaeiyan, Perfect 3- Colorings of the Johnson Graph J(6, 3). Bull. Iran. Math. Soc., (2020). https://doi.org/10.1007/s41980-019-00346-9. 4. H. Ansari-Toroghy; F. Farshadifar; F. Mahboobi-Abkenar. The small intersection graph relative to multiplication modules, J. Algebra Relat. Topics, (1) 4 (2016), 21-32. 5. S.V. Avgustinovich, I. Y. Mogilnykh, Perfect 2-colorings of Johnson graphs J(6,3) and J(7, 3), Lect. Notes Comput. Sci., 5228 (2008) 11-19. 6. S.V. Avgustinovich, I. Y. Mogilnykh, Perfect colorings of Johnson graphs J(8,3) and J(8, 4) with tow colors, J. Appl. Industrial Math., 5 (2011) 19-30. 7. D. G. Fon-Der-Flaass, A bound on correlation immunity, Sib. Electron. Math. Reports J., 4 (2007) 133-135. 8. D. G. Fon-Der-Flaass, Perfect 2-coloring of a hypercube, Sib. Math. J., 4 (2007) 923-930. 9. D. G. Fon-Der-Flaass, Perfect 2-coloring of a 12-dimensional cube that achive a bound of correlation immunity, Sib. Math. J., 4 (2007) 292-295. 10. C. Godsil, Compact graphs and equitable partitions, Linear Algebra Appl., 255 (1997) 259-266. | ||
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