Completely regular codes in the infinite hexagonal grid
  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. 
Sergey V. Avgustinovich (Sobolev Institute of Mathematics,   Novosibirsk, Russia), Denis S. Krotov (Sobolev Institute of Mat...
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