Nordhaus–Gaddum conjecture for power domination

Let $G$ be a graph of order $n$, and let $\overline{G}$ denote its complement. Assume that every component of both $G$ and $\overline{G}$ has order at least $3$. Write $\gamma_P(G)$ for the power domination number of $G$. Nordhaus–Gaddum conjecture for power domination.

$$\gamma_P(G)+\gamma_P(\overline{G})\le \left\lfloor\frac{n}{3}\right\rfloor+2.$$

The bound would show that the exceptional orders $13,14,16,17,20$ arising in the preceding result are not genuine exceptions. The paper notes that no counterexamples are known, while the conjecture remains unresolved.