Abstract

Let G be a simple undirected graph with n vertices and m edges. The energy of G, ∈(G) corresponds to the sum of its singular values. This work obtains lower bounds for ∈(G) where one of them generalizes a lower bound obtained by Mc Clelland in 1971 to the case of graphs with given nullity. An extension to the bipartite case is given and, in this case, it is shown that the lower bound 2√m is improved. The equality cases are characterized. Moreover, a simple lower bound that considers the number of edges and the diameter of G is derived. A simple lower bound, which improves the lower bound 2√n - 1, for the energy of trees with n vertices and diameter d is also obtained.