Goubko's BFS-tree conjecture for distance spectral radius

Let a tree degree sequence be fixed, and let $BFS(\mathbf{d})$ denote the breadth-first-search (greedy) tree generated by it. The BFS-tree conjecture for distance spectral radius. The tree $BFS(\mathbf{d})$ has the minimum distance spectral radius among all trees with degree sequence $\mathbf{d}$. This generalizes the conjecture of Stevanovic and Ilic for Volkmann trees; its status is not resolved in the source.