The coefficients of Laplacian characteristic polynomials of graphs

Li et al. [J.X. Li, W.C. Shiu, A. Chang, The number of spanning trees of a graph, Appl. Math. Lett. 23 (2010) 286–290] obtained some upper bounds for the number of spanning trees of graphs. In this paper, we characterize the connected graph G with the connectivity κ (resp. edge-connectivity κ′ and chromatic number χ) which has the maximal coefficients of the Laplacian characteristic polynomial. Since the number of spanning trees of a graph G is determined by one of the coefficients of the Laplacian characteristic polynomial of G, we generalize the results by Li et al.