ENRU
English version: Journal of Applied and Industrial Mathematics, 2017, 11:3, 381388 

Volume 24, No 3, 2017, P. 2034 UDC 519.174.7
Keywords: perfect coloring, circulant graph, equitable partition. DOI: 10.17377/daio.2017.24.559 Mariya A. Lisitsyna ^{1} Received 2 December 2016 References[1] S. V. Avgustinovich, A. Yu. Vasil’eva, and I. V. Sergeeva, Distance regular colorings of the infinite rectangular grid, Diskretn. Anal. Issled. Oper., 18, No. 3, 3–10, 2011 [Russian]. Translated in J. Appl. Ind. Math., 6, No. 3, 280–285, 2012.[2] S. V. Avgustinovich and M. A. Lisitsyna, Perfect 2colorings of transitive cubic graphs, Diskretn. Anal. Issled. Oper., 18, No. 2, 3–17, 2011 [Russian]. Translated in J. Appl. Ind. Math., 5, No. 4, 519–528, 2011. [3] M. A. Lisitsyna, Perfect 3colorings of prisms and Möbius ladders, Diskretn. Anal. Issled. Oper., 20, No. 1, 28–36, 2013 [Russian]. Translated in J. Appl. Ind. Math., 7, No. 2, 215–220, 2013. [4] M. A. Lisitsyna and S. V. Avgustinovich, Perfect colorings of the prism graph, Sib. Electron. Mat. Izv., 13, 1116–1128, 2016 [Russian]. [5] O. G. Parshina, Perfect 2colorings of infinite circulant graphs with continuous set of distances, Diskretn. Anal. Issled. Oper., 21, No. 2, 76–83, 2014 [Russian]. Translated in J. Appl. Ind. Math., 8, No. 3, 357–361, 2014. [6] S. A. Puzynina, Perfect colorings of vertices of the graph $G(Z^2)$ in three colors, Diskretn. Anal. Issled. Oper., Ser. 2, 12, No. 1, 37–54, 2005 [Russian]. [7] D. B. Khoroshilova, On twocolour perfect colourings of circular graphs, Diskretn. Anal. Issled. Oper., 16, No. 1, 80–92, 2009 [Russian]. [8] D. B. Khoroshilova, On the parameters of perfect 2colorings of circulant graphs, Diskretn. Anal. Issled. Oper., 18, No. 6, 82–89, 2011 [Russian]. [9] D. M. Cvetkovic, M. Doob, and H. Sachs, Spectra of Graphs: Theory and Application, VEB Dtsch. Verl. Wiss., Berlin, 1980. Translated under the title Spektry grafov: Teoriya i primenenie, Naukova Dumka, Kiev, 1984 [Russian]. [10] M. A. Axenovich, On multiple coverings of the infinite rectangular grid with balls of constant radius, Discrete Math., 268, No. 1–3, 31–48, 2003. [11] O. G. Parshina, Perfect $k$colorings of infinite circulant graphs with a continuous set of distances, in Abs. Int. Conf. PhD Summer Sch. “Groups and Graphs, Algorithms and Automata”, Yekaterinburg, Russia, Aug. 9–15, 2015, p. 80, UrFU Publ., Yekaterinburg, 2015. Available at http://g2a2.imm.uran.ru/doc/G2A2_Abstracts.pdf (accessed Apr. 16, 2017). [12] S. A. Puzynina and S. V. Avgustinovich, On periodicity of twodimensional words, Theor. Comput. Sci., 391, 178–187, 2008. 

© Sobolev Institute of Mathematics, 2015  