Computing some Laplacian Coefficients of Forests

Abstract

Let $G$ be a finite simple graph with Laplacian polynomial $\psi \left(G,\lambda \right)={\sum }_{k=0}^n{\left(-1\right)}^{n-k}{c}_k{\lambda }^k$ . In an earlier paper, the coefficients $c_{n-4}$ and $c_{n-5}$ for forests 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 coefficient $c_{n-6}$ .