Ning–Lu–Wang spectral-radius conjecture for edge connectivity

Let $\mathcal{A}_{n}^{\kappa',\delta}$ be the set of graphs of order $n$ with minimum degree $\delta$ and edge connectivity $\kappa'$. Let $B_{n,\delta+1}^{\kappa'}$ be the graph obtained from $K_{\delta+1}\cup K_{n-\delta-1}$ by adding $\kappa'$ edges joining one vertex in $K_{\delta+1}$ to $\kappa'$ vertices in $K_{n-\delta-1}$. Ning–Lu–Wang conjecture. For $4\leq\kappa'<\delta$, $B_{n,\delta+1}^{\kappa'}$ is the graph with the maximum spectral radius in $\mathcal{A}_{n}^{\kappa',\delta}$. The source says that this conjecture is settled by the paper's results, but the supplied excerpt does not state the exact resolving theorem or its hypotheses.