Bounds of Distance Estrada Index of Graphs

Abstract

Let \(\lambda_1, \lambda_2, \ldots, \lambda_n\) be the eigenvalues of the distance matrix of a connected graph \(G\). The distance Estrada index of \(G\) is defined as \(DEE(G) = \sum_{i=1}^{n} e^{\lambda_i}\). In this note, we present new lower and upper bounds for \(DEE(G)\). In addition, a Nordhaus-Gaddum type inequality for \(DEE(G)\) is given.