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

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

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...

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Main Authors: Yang Yang, Lizhu Sun, Changjiang Bu
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2020/3972789
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spelling doaj-32637769787a432788087bc24ba1bf9e2021-07-02T11:54:58ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/39727893972789A Note on Some Bounds of the α-Estrada Index of GraphsYang Yang0Lizhu Sun1Changjiang Bu2College of Automation, Harbin Engineering University, Harbin 150001, ChinaCollege of Mathematical Sciences, Harbin Engineering University, Harbin 150001, ChinaCollege of Automation, Harbin Engineering University, Harbin 150001, ChinaLet 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.http://dx.doi.org/10.1155/2020/3972789
collection DOAJ
language English
format Article
sources DOAJ
author Yang Yang
Lizhu Sun
Changjiang Bu
spellingShingle Yang Yang
Lizhu Sun
Changjiang Bu
A Note on Some Bounds of the α-Estrada Index of Graphs
Advances in Mathematical Physics
author_facet Yang Yang
Lizhu Sun
Changjiang Bu
author_sort Yang Yang
title A Note on Some Bounds of the α-Estrada Index of Graphs
title_short A Note on Some Bounds of the α-Estrada Index of Graphs
title_full A Note on Some Bounds of the α-Estrada Index of Graphs
title_fullStr A Note on Some Bounds of the α-Estrada Index of Graphs
title_full_unstemmed A Note on Some Bounds of the α-Estrada Index of Graphs
title_sort note on some bounds of the α-estrada index of graphs
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2020-01-01
description 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.
url http://dx.doi.org/10.1155/2020/3972789
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