A note on sum of powers of the Laplacian eigenvalues of bipartite graphs

For a graph G and a real number α≠0, the graph invariant sα(G) is the sum of the αth power of the non-zero Laplacian eigenvalues of G. In this note, we obtain some bounds of sα(G) for a connected bipartite graph G, which improve some known results of Zhou [B. Zhou, On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl. 429 (2008) 2239-2246].