  We show that for graph Laplacians $\Delta_G$ on a connected locally finite
simplicial undirected graph $G$ with countable infinite vertex set $V$ none of
the operators $\alpha\,\mathrm{Id}+\beta\Delta_G,
\alpha,\beta\in\mathbb{K},\beta \ne 0$, generate a strongly continuous
semigroup on $\mathbb{K}^V$ when the latter is equipped with the product
topology.
