2 problems

Let $G=(V,E)$) be the infinite king grid with vertex set $V=\mathbb{Z}\times\mathbb{Z}$, in which two vertices are adjacent exactly when their Euclidean distance is at most…

Let $\mathcal{K}_n=P_n\boxtimes P_n$ be the King grid, where $P_n$ is the path on $n$ vertices. Write $\gamma^*_e(G)$ for the minimum cardinality of an exponential dominating set i…