An increasing sequence of lower bounds for the Estrada index of graphs and matrices

Abstract

Let G be a graph on n vertices and λ1≥λ2≥…≥λn its eigenvalues. The Estrada index of G is defined as EE(G)=∑i=1neλi. In this work, we use an increasing sequence converging to the λ1 to obtain an increasing sequence of lower bounds for EE(G). In addition, we generalize this succession for the Estrada index of an arbitrary symmetric nonnegative matrix.