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arXiv · 1612.01360

Completely regular codes in the infinite hexagonal grid

Sergey V. Avgustinovich·Denis S. Krotov·Anastasia Yu. Vasil'eva
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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.

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Sergey V. Avgustinovich, Denis S. Krotov, Anastasia Yu. Vasil'eva. 2016-11-30. Completely regular codes in the infinite hexagonal grid. https://doi.org/10.17377/semi.2016.13.079

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