A Note on Some Bounds of the α-Estrada Index of Graphs. (16th March 2020) - Yang, Yang; Sun, Lizhu; Bu, Changjiang
Abstract : Let G be a simple graph with n vertices. Let A α G = α D G + 1 − α A G, where 0 ≤ α ≤ 1 and A G and D G denote the adjacency matrix and degree matrix of G, respectively. E E α G = ∑ i = 1 n e λ i is called the α -Estrada index of G, where λ 1, ⋯, λ n denote the eigenvalues of A α G . In this paper, the upper and lower bounds for E E α G are given. Moreover, some relations between the α -Estrada index and α -energy are established.