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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, thecoefficients $c_{n-4}$ and $c_{n-5}$ for tree with respect to some degree-basedgraph invariants were computed. The aim of this paper is to continue this workby giving an exact formula for the coefficients $c_{n-6}$. As a consequence ofthis work, the Laplacian coefficients $c_{n-k}$ of a forest $F$, $1\leq k \leq6$, are computed in terms of the number of closed walks in $F$ and its linegraph.

Laplacian Coefficients of a Forest in terms of the Number of Closed Walks in the Forest and its Line Graph