New lower bounds for the Estrada and Signless Laplacian Estrada Index of a Graph

Let $G$ be a graph on $n$ vertices and ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{\lambda_i}.$ In this work, using a different demonstration technique, new lower bounds are obtained for the Estrada index, that depends on the number of vertices, the number of edges and the energy of the graph is given. Moreover, another lower bound for the Estrada index is obtained of an arbitrary non-negative Hermitian matrix are established.