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Investigating 1-perfect code using Dominating set | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 479-483 اصل مقاله (482.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.18237.1997 | ||
| نویسندگان | ||
| Fatemeh Halataei* 1؛ saeed Mohammadian2 | ||
| 1Faculty of Mathematics, Statistics, and Computer Science, Semnan University, Semnan, Iran | ||
| 2Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran | ||
| تاریخ دریافت: 19 تیر 1398، تاریخ پذیرش: 02 مهر 1398 | ||
| چکیده | ||
| In this article, we investigate the relation between dominating sets and 1-perfect codes. We also study perfect colorings of some Johnson graphs in two colors using linear programming problem. | ||
| کلیدواژهها | ||
| Perfect 2-coloring؛ 1- perfect code؛ Dominating set؛ Johnson graph | ||
| مراجع | ||
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[1] S. V. Avgustinovich and I. Yu.Mogil’nykh, Perfect colorings of the Johnson graphs J(8, 3) and J(8, 4) with two colors, J. Appl. Ind. Math. 5(1) (2011) 19–30. [2] S. V. Avgustinovich and M. A. Lisitsyna, Perfect 2-Colorings of Transitive Cubic Graphs, J. Appl. Ind. Math. (2011) 519-528. [3] N. Biggs, Algebraic Graph Theory, Cambridge University Press, England, 1974. [4] D. B. Khoroshilova, On circular perfect colorings with two colors, Diskret. Anal. Issled. Oper. 16 (2009) 80–92. [5] I. Yu. Mogilnykh and S. V. Avgustinovich, Perfect 2-Colorings of Johnson Graphs J(6, 3) and J(7, 4) , Lecture Notes in Computer Science, Vol. 5228, Springer, Berlin, 2008. [6] K. V. Vorob’ev and D. G. Fon-der-Flaass, On perfect 2-colorings of a hypercube, Siberian Elect.. Mat. Izv. 7 (2010) 65–75. [7] D. B. West, Introduction to Graph Theory, University of Illinois – Urbana, 2002. | ||
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