Tree sigma_t-irregularity inequality conjecture

Let $T$ be an $n$-vertex tree, and let $\sigma(T)$ and $\sigma_t(T)$ denote its Albertson irregularity and $\sigma_t$-irregularity, respectively. Let $P_n$ be the path on $n$ vertices.

Tree irregularity inequality conjecture.

$$\sigma_t(T)\leq (n-2)\sigma(T).$$

Equality holds if and only if $T$ is $P_n$.

The conjecture asks for an upper bound relating the modified irregularity to the Albertson irregularity for every tree on $n$ vertices, together with a characterization of the equality case. The supplied text does not state whether it has been resolved.