Laplacian coefficients and Zagreb indices of trees

Let G be a simple and undirected graph with Laplacian polynomial ψ(G,λ)=∑k=0n(-1)n-kck(G)λk. In earlier works, some formulas for computing c2(G), cn-2(G) and cn-3(G) in terms of the number of vertices, the Wiener, the first Zagreb and the forgotten indices are given. In this paper, we continue this work by computing cn-4(T), where T is a tree. A lower and an upper bound for cn-4(T) are obtained.