On Independent Domination in Direct Products

In [16] Nowakowski and Rall listed a series of conjectures involving several different graph products. particular, they conjectured that $$i(G\times H) \ge i(G)i(H)$$ where i(G) is the independent domination number G $$G\times H$$ direct product graphs H. We show this conjecture false, and, in fact, construct pairs for which $$\min \{i(G), i(H)\} - i(G\times H)$$ arbitrarily large. also give exact value K_n)$$ when either path or cycle.