On spectral moments and energy of graphs

Let G be a graph on n vertices, and let lambda(1), lambda(2),..., lambda(n) be its eigenvalues. The energy of G is E = Sigma(n)(i=1) vertical bar lambda(i)vertical bar. The k-th spectral moment of G is M-k = Sigma(n)(i=1) (lambda(i))(k). We prove that for even positive integers r, s, t, such that 4r = s + t + 2, the inequality E >= (M-r)(2) /root MsMt holds for all graphs with at least one edge, thus generalizing ail earlier result.