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 Q(G)=Tr(G)+D(G), where D(G) is the distance matrix, Tr(G)=diag(D1,D2,…,Dn) and Di is the row sum of D(G) corresponding to vertex vi. Denote by ρD(G), ρminD(G) the largest eigenvalue and the least eigenvalue of D(G), respectively. And denote by qD(G), qminD(G) the largest eigenvalue and the least eigenvalue of Q(G), respectively. The distance spread of a graph G is defined as SD(G)=ρD(G)−ρminD(G), and the distance signless Laplacian spread of a graph G is defined as SQ(G)=qD(G)−qminD(G). In this paper, we point out an error in the result of Theorem 2.4 in Yu et al. (2012) and modify it. As well, we obtain some lower bounds on distance signless Laplacian spread of a graph.