A Note on Some Bounds of the α-Estrada Index of Graphs

Abstract EN

Let G be a simple graph with n vertices.

Let A~αG=αDG+1−αAG, where 0≤α≤1 and AG and DG denote the adjacency matrix and degree matrix of G, respectively.

EEαG=∑i=1neλi is called the α-Estrada index of G, where λ1,⋯,λn denote the eigenvalues of A~αG.

In this paper, the upper and lower bounds for EEαG are given.

Moreover, some relations between the α-Estrada index and α-energy are established.