Laplacian coefficients of trees

Let G be a simple and undirected graph with Laplacian polynomial ψ(G, λ) = Σk=0n (−1)n-kck(G)λk. In this paper, exact formulas for the coefficient cn−4 and the number of 4-matchings with respect to the Zagreb indices of a given tree are presented. The chemical trees with first through the fifteenth greatest cn−4-values are also determined