On the Laplacian coefficients of unicyclic graphs

Let G be a graph of order n and let P(G, gimel) = Sigma(n)(k=o)(-1)C-k(k)lambda(n-k) be the characteristic polynomial of its Laplacian matrix. Generalizing an approach of Mohar on graph transformations, we show that among all connected unicyclic graphs of order n, the kth coefficient C-k is largest when the graph is a cycle C-n and smallest when the graph is the a S-n with an additional edge between two of its pendent vertices. A relation to the recently established Laplacian-like energy of a graph is discussed. (C) 2008 Elsevier Inc. All rights reserved.