On the Laplacian coefficients of unicyclic graphs

Abstract Let G be a graph of order n and let P ( G , λ ) = ∑ k = 0 n ( - 1 ) k c k λ 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 k th 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.