Multilattice graphs and perfect domination
Perfect codes in the $n$-dimensio\-nal grid $Λ_n$ of the lattice $\mathbb{Z}^n$ ($0 2$ with radius $n$.
math.CO↗
arXiv subjects
Luis R. Fuentes
Publications and source records attributed to Luis R. Fuentes.
There is but one PDS in $\mathbb{Z}^{3}$ inducing just square components
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.
math.CO↗