On the Laplacian coefficients of acyclic graphs Original Research Article

Let G be a graph of order n and let image be the characteristic polynomial of its Laplacian matrix. Zhou and Gutman recently proved that among all trees of order n, the kth coefficient ck is largest when the tree is a path, and is smallest for stars. A new proof and a strengthening of this result is provided. A relation to the Wiener index is discussed.