Distance and distance signless Laplacian spread of connected graphs

For a connected graph $G$ on $n$ vertices, recall that the distance signless Laplacian matrix of $G$ is defined to be $mathcal{Q}(G)=Tr(G)+mathcal{D}(G)$, where $mathcal{D}(G)$ is the distance matrix, $Tr(G)=diag(D_1, D_2, ldots, D_n)$ and $D_{i}$ is the row sum of $mathcal{D}(G)$ corresponding to vertex $v_{i}$. Denote by $rho^{mathcal{D}}(G),$ $rho_{min}^{mathcal{D}}(G)$ the largest eigenvalue and the least eigenvalue of $mathcal{D}(G)$, respectively. And denote by $q^{mathcal{D}}(G)$, $q_{min}^{mathcal{D}}(G)$ the largest eigenvalue and the least eigenvalue of $mathcal{Q}(G)$, respectively. The distance spread of a graph $G$ is defined as $S_{mathcal{D}}(G)=rho^{mathcal{D}}(G)- rho_{min}^{mathcal{D}}(G)$, and the distance signless Laplacian spread of a graph $G$ is defined as $S_{mathcal{Q}}(G)=q^{mathcal{D}}(G)-q_{min}^{mathcal{D}}(G)$. In this paper, we point out an error in the result of Theorem 2.4 in Distance spectral spread of a graph [G.L. Yu, et al, Discrete Applied Mathematics. 160 (2012) 2474--2478] and rectify it. As well, we obtain some lower bounds on ddistance signless Laplacian spread of a graph.