Abstract

Let G be a simple undirected graph with n vertices, m edges, adjacency matrix A, largest eigenvalue rho and nullity kappa. The energy of G, epsilon(G) is the sum of its singular values. In this work lower bounds for epsilon(G) in terms of the coefficient of mu(kappa) in the expansion of characteristic polynomial, p(mu) = det (mu I - A) are obtained. In particular one of the bounds generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in 2013 to the case of graphs with given nullity. The bipartite case is also studied obtaining in this case, a sufficient condition to improve the spectral lower bound 2 rho. Considering an increasing sequence convergent to rho a convergent increasing sequence of lower bounds for the energy of G is constructed.