  Let $G$ be a simple connected simple graph of order $n$. The distance
Laplacian matrix $D^{L}(G)$ is defined as $D^L(G)=Diag(Tr)-D(G)$, where
$Diag(Tr)$ is the diagonal matrix of vertex transmissions and $D(G)$ is the
distance matrix of $G$. The eigenvalues of $D^{L}(G)$ are the distance
Laplacian eigenvalues of $G$ and are denoted by $\partial_{1}^{L}(G),
\partial_{2}^{L}(G),\dots,\partial_{n}^{L}(G)$. The \textit{ distance Laplacian
spread} $DLS(G)$ of a connected graph $G$ is the difference between largest and
second smallest distance Laplacian eigenvalues, that is,
$\partial_{1}^{L}(G)-\partial_{n-1}^{L}(G)$. We obtain bounds for $DLS(G)$ in
terms of the Wiener index $W(G)$, order $n$ and the maximum transmission degree
$Tr_{max}(G)$ of $G$ and characterize the extremal graphs. We obtain two lower
bounds for $DLS(G)$, the first one in terms of the order, diameter and the
Wiener index of the graph, and the second one in terms of the order, maximum
degree and the independence number of the graph. For a connected $ k-partite$
graph $G$, $k\leq n-1$, with $n$ vertices having disconnected complement, we
show that
  $ DLS(G)\geq \Big \lfloor \frac{n}{k}\Big \rfloor$ with equality if and only
if $G$ is a $complete ~ k-partite$ graph having cardinality of each independent
class same and $n \equiv 0 \pmod k$.
