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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
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
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
Linking options:
https://www.mathnet.ru/eng/semr728 https://www.mathnet.ru/eng/semr/v13/p987
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