  Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Let
$Tr(G)$ be the diagonal matrix of vertex transmissions of $G$ and $D(G)$ be the
distance matrix of $G$. The distance Laplacian matrix of $G$ is defined as
$\mathcal{L}(G)=Tr(G)-D(G)$. The distance signless Laplacian matrix of $G$ is
defined as $\mathcal{Q}(G)=Tr(G)+D(G)$. In this paper, we give a lower bound on
the distance Laplacian spectral radius in terms of $D_1$, as a consequence, we
show that $\partial_1^L(G)\geq n+\lceil\frac{n}{\omega}\rceil$ where $\omega$
is the clique number of $G$. Furthermore, we give some graft transformations,
by using them, we characterize the extremal graph attains the maximum distance
spectral radius in terms of $n$ and $\omega$. Moreover, we also give bounds on
the distance signless Laplacian eigenvalues of $G$, and give a confirmation on
a conjecture due to Aouchiche and Hansen.
