Geodesic
Completely regular codes in the infinite hexagonal grid
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 987-1016

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : equitable partition, partition design, hexagonal grid. 
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     author = {S. V. Avgustinovich and D. S. Krotov and A. Yu. Vasil'eva},
     title = {Completely regular codes in the infinite hexagonal grid},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {987--1016},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a64/}
}
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S. V. Avgustinovich; D. S. Krotov; A. Yu. Vasil'eva. Completely regular codes in the infinite hexagonal grid. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 987-1016. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a64/