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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 987–1016
DOI: https://doi.org/10.17377/semi.2016.13.079
(Mi semr728)
 

This article is cited in 4 scientific papers (total in 4 papers)

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
References:
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.
Received April 15, 2016, published November 15, 2016
Bibliographic databases:
Document Type: Article
UDC: 519.148
MSC: 05B99
Language: English
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
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\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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000407781100079}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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