Upper-bound conjecture for the d-distance p-packing domination number of trees

Let $T$ be a tree of order $n$, and let $d$ and $p$ be integers satisfying

$$3 \leq p \leq d.$$

Here, $\gamma_d^p(T)$ denotes the $d$-distance $p$-packing domination number of $T$.

Tree upper-bound conjecture. If $3 \leq p \leq d$, then

$$\gamma_d^p(T) \leq \frac{n-2\sqrt{n}+d+1}{d}.$$

This conjecture extends the cited upper bound for $\gamma_d^1(G)$ and the paper's preceding result for trees when $p=2$. Its status is not established in the supplied source context.