On the Laplacian Coefficients of Trees

Abstract

Let G be a finite simple graph with Laplacian polynomial ψ(G,λ) = ∑ k=0n(−1)n−kck(G)λk. In an earlier paper, we computed the coefficient of cn−4 for trees with respect to some degree-based graph invariant. The aim of this paper is to continue this work by giving an exact formula for the coefficient cn−5 in the polynomial ψ(G,λ). As a consequence of this work, the Laplacian coefficients cn−k, k = 2, 3, 4, 5, for some know trees were computed.