On generalized adjacency Estrada index of graphs

The Estrada index is a graph-spectrum-based invariant having an important role in chemistry and physics. In this paper, we define the generalized adjacency Estrada index of a graph and obtain some lower and upper bounds for the generalized adjacency Estrada index in terms of various graph parameters associated with the structure of a graph. Further, we characterize the extremal graphs attaining these bounds. We also highlight the relationship between generalized adjacency Estrada index and generalized adjacency energy. Using these results, we obtain the improved bounds for the Estrada index based on the adjacency eigenvalues of a graph.