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(D-1, D-2,...,D-n) and D-i is the row sum of D(G) corresponding to vertex v(i). Denote by p(D)(G), p(min)(D),(G) the largest eigenvalue and the least eigenvalue of D(G), respectively. And denote by q(D)(G), q(min)(D)(G) the largest eigenvalue and the least eigenvalue of Q(G), respectively. The distance spread of a graph G is defined as S-D(G) = p(D)(G) - p(min)(D)(G), and the distance signless Laplacian spread of a graph G is defined as S-Q(G) = q(D)(G) - q(min)(D)(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. (C) 2017 Elsevier B.V. All rights reserved.