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

Abstract

Let $G$ be a graph on $n$ vertices and ${\lambda }_1\ge {\lambda }_2\ge \dots \ge {\lambda }_n$ 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.

arXiv admin note: text overlap with arXiv:1810.04120