Chen–Dehmer–Shi's extremal entropy conjecture for trees

Let $T$ be a tree with $n$ vertices. Let $S_{\lfloor n/2\rfloor,\lceil n/2\rceil}$ be the balanced double star, and let $CS(n,t)$ denote a comet; write $t_0$ for the parameter specified by the conjecture. The entropy under consideration is $I_{f^n_2}$.

Chen–Dehmer–Shi's conjecture. The balanced double star and the comet $CS(n,t_0)$ attain the maximum and minimum values of $I_{f^n_2}(T)$, respectively.

The conjecture is motivated by the preceding comparison between the star, path and balanced double star and by the proposed extremal role of the comet. The source does not provide a proof or a resolution.