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

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