Strength–super edge-magic deficiency conjecture for trees

Let $T$ be a nontrivial tree. A numbering of $T$ is a bijection $f:V(T)\to\{1,2,\ldots,|V(T)|\}$, and its strength is

$$\operatorname{str}_f(T)=\max\{f(u)+f(v):uv\in E(T)\}.$$

The strength of $T$ is

$$\operatorname{str}(T)=\min_f\operatorname{str}_f(T),$$

where the minimum is over all numberings, and $\mu_s(T)$ denotes the super edge-magic deficiency of $T$. Strength–super edge-magic deficiency conjecture. For every nontrivial tree $T$, there exists some positive constant $c$ such that

$$\operatorname{str}(T)\geq c\cdot\mu_s(T)+|V(T)|+1.$$

The paper notes that the known equality $\operatorname{str}(T)=|V(T)|+1$ for every nontrivial tree would make this conjecture imply the conjecture that every nontrivial tree is super edge-magic. Its status is not resolved in the source.