There is but one PDS in ${\mathbb{Z}}^3$ inducing just square components

Italo J. Dejter, Luis R. Fuentes, Carlos A. Araujo

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 v…