For any real number α, the general energy of a graph is defined as the sum of the α-th powers of the nonzero singular values of its adjacency matrix. This definition unifies several classical spectral invariants, such as the graph energy and spectral moments. In this paper, we establish bounds on the general energy of graphs. These bounds, in turn, yield new estimates for the ordinary energy and spectral moments, and lead to a more general relationship between these quantities.
