  Let $G$ be a simple graph with $n$ vertices and let $\mu_1 \geqslant \mu_2
\geqslant...\geqslant \mu_{n - 1} \geqslant \mu_n = 0$ be the eigenvalues of
its Laplacian matrix. The Laplacian Estrada index of a graph $G$ is defined as
$LEE (G) = \sum\limits_{i = 1}^n e^{\mu_i}$. Using the recent connection
between Estrada index of a line graph and Laplacian Estrada index, we prove
that the path $P_n$ has minimal, while the star $S_n$ has maximal $LEE$ among
trees on $n$ vertices. In addition, we find the unique tree with the second
maximal Laplacian Estrada index.

Combinatorics