Claw-free regular graph power domination conjecture

Let $l\ge 1$ and $k\ge l$ be integers, and let $G$ be a connected claw-free $(k+l+1)$-regular graph of order $n$. Let $\gamma_{p,k}(G)$ denote the minimum cardinality of a $k$-power dominating set of $G$. Claw-free regular graph power domination conjecture. Then

$$\gamma_{p,k}(G)\le \frac{n}{k+l+2},$$

and this bound is tight. The construction $C_{k,t}$ described in the source shows tightness for the relevant parameters. The conjecture is stated to remain open when $l\ge 4$.