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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 987–1016 (Mi semr728)  

This article is cited in 1 scientific paper (total in 1 paper)

Discrete mathematics and mathematical cybernetics

Completely regular codes in the infinite hexagonal grid

S. V. Avgustinovich, D. S. Krotov, A. Yu. Vasil'eva

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: A set $C$ of vertices of a simple graph is called a completely regular code if for each $i=0$, $1$, $2, \ldots$ and $j = i-1$, $i$, $i+1$, all vertices at distance $i$ from $C$ have the same number $s_{ij}$ of neighbors at distance $j$ from $C$. We characterize the completely regular codes in the infinite hexagonal grid graph.

Keywords: completely regular code, perfect coloring, equitable partition, partition design, hexagonal grid.

DOI: https://doi.org/10.17377/semi.2016.13.079

Full text: PDF file (1935 kB)
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Bibliographic databases:

UDC: 519.148
MSC: 05B99
Received April 15, 2016, published November 15, 2016
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Citation: S. V. Avgustinovich, D. S. Krotov, A. Yu. Vasil'eva, “Completely regular codes in the infinite hexagonal grid”, Sib. Èlektron. Mat. Izv., 13 (2016), 987–1016

Citation in format AMSBIB
\Bibitem{AvgKroVas16}
\by S.~V.~Avgustinovich, D.~S.~Krotov, A.~Yu.~Vasil'eva
\paper Completely regular codes in the infinite hexagonal grid
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 987--1016
\mathnet{http://mi.mathnet.ru/semr728}
\crossref{https://doi.org/10.17377/semi.2016.13.079}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000407781100079}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. Borges, J. Rifà, V. A. Zinoviev, “On completely regular codes”, Problems Inform. Transmission, 55:1 (2019), 1–45  mathnet  crossref  crossref  isi  elib
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