The star graph maximizer conjecture for entanglement of formation

Let $\mathcal{G}_{n}^{c}$ be the set of all connected graphs on $n$ vertices, and let $G\in\mathcal{G}_{n}^{c}$ with $|V|=pq$. Star graph maximizer conjecture.

$$\max_{\mathcal{G}_{n}^{c}} E_{F}(\sigma(G))=E_{F}(\sigma(K_{1,n-1})).$$

This asserts that the star graph maximizes the entanglement of formation among connected graph density matrices on $n$ vertices. The source provides no resolution, so the conjecture remains open.