  Signless Laplacian Estrada index of a graph $G$, defined as
$SLEE(G)=\sum^{n}_{i=1}e^{q_i}$, where $q_1, q_2, \cdots, q_n$ are the
eigenvalues of the matrix $\mathbf{Q}(G)=\mathbf{D}(G)+\mathbf{A}(G)$. We
determine the unique graphs with maximum signless Laplacian Estrada indices
among the set of graphs with given number of cut edges, pendent vertices,
(vertex) connectivity and edge connectivity.
