Bounds for the Distance Estrada Index of Graphs

Let G be simple connected graph with n vertices. The distance eigenvalues mu(1) >= mu(2) >= ... >= mu(n) of G are the eigenvalues of its distance matrix D(G). The distance Estrada index of G is defined as DEE(G) = Sigma(n)(i=1) e(mu) [14]. In this paper, we establish better lower bounds for DEE (G) as well as some relations between DEE(G) and the distance energy.