Dehmer–Kraus–Schaumann's minimal dendrimer entropy conjecture

Let $D$ be a dendrimer on $n$ vertices, with orbit weights $c_i$ satisfying $c_i=c_j$ whenever $i\neq j$. Let $I_{f^3}(D)$ denote the corresponding entropy; the star graph has radius $r=1$ and progressive degree $p=n-2$.

Dehmer–Kraus–Schaumann's conjecture. The star graph has the minimal value of $I_{f^3}(D)$.

This is a second conjecture on extremal dendrimer entropy, proposed in the cited work for the stated class of weight sequences. The supplied source gives no proof or resolution.