Some New Lower Bounds for the Estrada Index

Abstract: Let $G$ be a graph on $n$ vertices and $\lambda_1,\lambda_2,\ldots,\lambda_n$ its eigenvalues. The Estrada index of $G$ is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. In this paper, we present some new lower bounds obtained for the Estrada Index of graphs and in particular of bipartite graphs that only depend on the number of vertices, the number of edges, Randi\'c index, maximum and minimum degree and diameter.