Alev's completeness conjecture for the constructed B_n graph solutions

Let $B_n$ be the type-$B_n$ case, and consider the equation referred to in the source as Equation. Starting from the simple graphs and applying the construction described immediately before the conjecture, one obtains $\pi(n)$ graphs, where $\pi(n)$ denotes the number of partitions of $n$.

Alev's completeness conjecture. For every integer $n\geq 2$, these $\pi(n)$ constructed graphs are the only solutions of the equation.

The claim would classify all solutions in the $B_n$ case by the preceding graph construction. No general proof or disproof is supplied in the source.