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

Advances in Mathematical Physics

Yang Yang¹  Changjiang Bu²  Lizhu Sun³ 

[1] College of Automation, Harbin Engineering University, Harbin 150001, China, hrbeu.edu.cn;College of Automation, Harbin Engineering University, Harbin 150001, China, hrbeu.edu.cn;College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China, hrbeu.edu.cn;College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China, hrbeu.edu.cn;

DOI  :  10.1155/2020/3972789

来源: publisher

【 摘 要 】

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.

【 授权许可】

Unknown