A Note on Some Bounds of the α-Estrada Index of Graphs. (16th March 2020)

• Record Type: Journal Article
• Authors: Yang, Yang; Sun, Lizhu; Bu, Changjiang
• Other Names: Raymond Laurent Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2020(2020)
• Publication Date: 2020-03-16
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2020/3972789
• Languages: English
• ISSNs: 1687-9120

Abstract

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.