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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 590–603
DOI: https://doi.org/10.33048/semi.2020.17.038
(Mi semr1233)
 

This article is cited in 5 scientific papers (total in 5 papers)

Discrete mathematics and mathematical cybernetics

The perfect $2$-colorings of infinite circulant graphs with a continuous set of odd distances

O. G. Parshinaa, M. A. Lisitsynab

a Czech Technical University in Prague, 13, Trojanova, Prague, 120 00, Czech Republic
b Marshal Budyonny Military Academy of Telecommunications, 3, Tikhoretskii ave., St. Petersburg, 194064, Russia
Full-text PDF (642 kB) Citations (5)
References:
Abstract: A vertex coloring of a given simple graph $G=(V,E)$ with $k$ colors ($k$-coloring) is a map from its vertex set to the set of integers $\{1,2,3,\dots, k\}$. A coloring is called perfect if the multiset of colors appearing on the neighbours of any vertex depends only on the color of the vertex. We consider perfect colorings of Cayley graphs of the additive group of integers with generating set $\{1,-1,3,-3,5,-5,\dots, 2n-1,1-2n\}$ for a positive integer $n$. We enumerate perfect $2$-colorings of the graphs under consideration and state the conjecture generalizing the main result to an arbitrary number of colors.
Keywords: perfect coloring, circulant graph, Cayley graph, equitable partition.
Funding agency Grant number
Agence Nationale de la Recherche ANR-10-LABX-0070
ANR-11-IDEX-0007
Russian Foundation for Basic Research 18-31-00009
This work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d'Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR), and has been supported by RFBS grant 18-31-00009.
Received February 2, 2020, published April 17, 2020
Bibliographic databases:
Document Type: Article
UDC: 519.87
MSC: 05C15
Language: English
Citation: O. G. Parshina, M. A. Lisitsyna, “The perfect $2$-colorings of infinite circulant graphs with a continuous set of odd distances”, Sib. Èlektron. Mat. Izv., 17 (2020), 590–603
Citation in format AMSBIB
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\by O.~G.~Parshina, M.~A.~Lisitsyna
\paper The perfect $2$-colorings of infinite circulant graphs with a continuous set of odd distances
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 590--603
\mathnet{http://mi.mathnet.ru/semr1233}
\crossref{https://doi.org/10.33048/semi.2020.17.038}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000529942000001}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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