The generalized distance spectral radius conjecture for digraphs

Let $n,k$ be positive integers, let $0<\alpha<1$, and let $G\in\mathcal{G}_{n,k}$. Here, $\mu_\alpha(G)$ denotes the generalized distance spectral radius of $G$, and $K(n,k,1)$ is the specified extremal digraph in the paper. Generalized distance spectral radius conjecture. One has

$$\mu_\alpha(G)\geq\mu_\alpha(K(n,k,1)),$$

with equality if and only if $G\cong K(n,k,1)$. This conjecture proposes the extremal characterization for the general case, extending the cases established earlier in the paper; its resolution is not supplied in the source.