Nowakowski's independent domination conjecture for categorical graph products

Let $G$ and $H$ be graphs, and let $i(G)$ denote the smallest cardinality of an independent dominating set in $G$, equivalently the cardinality of a smallest maximal independent set. Nowakowski's conjecture. For all graphs $G$ and $H$,

$$i(G\times H)\geq i(G)\cdot i(H).$$

This conjecture asks whether the independent domination number is supermultiplicative under the categorical product. It is cited in the source as an existing conjecture, and no resolution status is supplied.