Bose et al.'s maximum distance spectral radius conjecture for cacti

Let $\mathcal{C}(n,k)$ be the class of all cacti on $n$ vertices and $k$ cycles, where $0\leq k\leq\lfloor\frac{n-1}{2}\rfloor$. Let $S(p,q;\ell)$ denote the saw-graph obtained by joining an end of a proper saw-graph of length $p$ with an end of another proper saw-graph of length $q$ by a path of length $\ell$.

Bose et al.'s conjecture. The graph

$$S\left(\left\lfloor\frac{k}{2}\right\rfloor,\left\lceil\frac{k}{2}\right\rceil;n-2k-1\right)$$

uniquely maximizes the distance spectral radius in $\mathcal{C}(n,k)$.

This conjecture proposes the extremal cactus for each permitted number of vertices and cycles. The source presents it as a conjecture based on computer results; its resolution is not specified here.