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

For a graph GG and a real number α≠0α≠0, the graph invariant sα(G)sα(G) is the sum of the ααth power of the non-zero Laplacian eigenvalues of GG. This note presents some bounds for sα(G)sα(G) in terms of the vertex degrees of GG, and a relation between sα(G)sα(G) and the first general Zagreb index, which is a useful topological index and has important applications in chemistry.