On the Laplacian coefficients of bicyclic graphs

Let G be a graph of order n and let P(G, x) = Sigma(n)(k=0)(-1)(k)c(k)x(n-k) be the characteristic polynomial of its Laplacian matrix. Generalizing the approach in [D. Stevanovic, A. Ilic, On the Laplacian coefficients of unicyclic graphs, Linear Algebra and its Applications 430 (2009) 2290-2300.] on graph transformations, we show that among all bicyclic graphs of order n, the kth coefficient c(k) is smallest when the graph is B-n (obtained from C-4 by adding one edge connecting two non-adjacent vertices and adding n 4 pendent vertices attached to the vertex of degree 3). (C) 2010 Elsevier B.V. All rights reserved.