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

Let $G$ be a graph on $n$ vertices and $\lambda_1\geq \lambda_2\geq \ldots \geq \lambda_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{\lambda_i}.$ In this work, we using an increasing sequence converging to the $\lambda_1$ to obtain an increasing sequence of lower bounds for $EE(G)$. In addition, we generalize this succession for the Estrada index of an arbitrary nonnegative Hermitian matrix.