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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/3972789 |
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| author | Yang Yang Lizhu Sun Changjiang Bu |
| author_facet | Yang Yang Lizhu Sun Changjiang Bu |
| author_sort | Yang Yang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-32637769787a432788087bc24ba1bf9e |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-32637769787a432788087bc24ba1bf9e2025-02-03T06:06:42ZengWileyAdvances 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 |
| spellingShingle | Yang Yang Lizhu Sun Changjiang Bu A Note on Some Bounds of the α-Estrada Index of Graphs Advances in Mathematical Physics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2020/3972789 |
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