  Let $G$ be a finite simple graph with Laplacian polynomial
$\psi(G,\lambda)=\sum_{k=0}^n(-1)^{n-k}c_k\lambda^k$. In an earlier paper, the
coefficients $c_{n-4}$ and $c_{n-5}$ for tree with respect to some degree-based
graph invariants were computed. The aim of this paper is to continue this work
by giving an exact formula for the coefficients $c_{n-6}$. As a consequence of
this work, the Laplacian coefficients $c_{n-k}$ of a forest $F$, $1\leq k \leq
6$, are computed in terms of the number of closed walks in $F$ and its line
graph.
