On the Laplacian coefficients of bicyclic graphs

Let G be a graph of order n and let be the characteristic polynomial of its Laplacian matrix. Generalizing the approach in D. Stevanovi?, A. Ili?, 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 C₄ by adding one edge connecting two non-adjacent vertices and adding n−4 pendent vertices attached to the vertex of degree 3).