There is but one PDS in mathbb{Z}³ inducing just square components
classification
🧮 math.CO
keywords
mathbbcomponentsthereuniquecyclesdistancedominatingexists
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It is known that in the unit distance graph of the lattice $\mathbb{Z}^3\subset\mathbb{R}^3$ there exists a dominating set $S$ with $4$-cycles as sole induced components and each vertex of $\mathbb{Z}^3\setminus S$ having a unique neighbor in $S$. We show $S$ is unique.
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