  Suppose that the vertex set of a connected graph $G$ is
$V(G)=\{v_1,\cdots,v_n\}$. Then we denote by $Tr_{G}(v_i)$ the sum of distances
between $v_i$ and all other vertices of $G$. Let $Tr(G)$ be the $n\times n$
diagonal matrix with its $(i,i)$-entry equal to $Tr_{G}(v_{i})$ and $D(G)$ be
the distance matrix of $G$. Then $Q_{D}(G)=Tr(G)+D(G)$ is the distance signless
Laplacian matrix of $G$. The largest eigenvalues of $Q_D(G)$ is called distance
signless Laplacian spectral radius of $G$. In this paper we give some graft
transformations on distance signless Laplacian spectral radius of the graphs
and use them to characterize the graphs with the minimum and maximal distance
signless Laplacian spectral radius among non-starlike and non-caterpillar
trees.
