laplacian‎ ‎coefficients of a‎ ‎forest in terms of the number of closed walks in the forest and its line graph

In this paper, we deal with calculating the laplacian coefficients of a finite simple graph g with the laplacian polynomial ψ(g, λ) = ∑n k=0(−1)n−k ckλ k . we also explore the relationship between the number of closed walks in a graph and a series of its line graphs with the laplacian coefficients. our objective is to find a way to determine the laplacian coefficients using the number of closed walks in a graph and its line graph. specifically, we have derived the laplacian coefficients cn−k of a forest f (where 1 ≤ k ≤ 6) in terms of the number of closed walks in f and its line graph.