Abstract

Let G be a simple undirected graph with n vertices, m edges, adjacency matrix A, largest eigenvalue ρ and nullity κ. The energy of G, ∈(G) is the sum of its singular values. In this work lower bounds for ∈(G) in terms of the coefficient of μκin the expansion of characteristic polynomial, p(μ) = det (μI - 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 2ρ. Considering an increasing sequence convergent to ρ a convergent increasing sequence of lower bounds for the energy of G is constructed.