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

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  • Yang Yang
  • Lizhu Sun
  • Changjiang Bu

Abstract

Let G be a simple graph with n vertices. Let A~αG=αDG+1−αAG, where 0 ≤ α ≤ 1 and A(G) and D(G) 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 EEα(G) are given. Moreover, some relations between the α‐Estrada index and α‐energy are established.

Suggested Citation

  • Yang Yang & Lizhu Sun & Changjiang Bu, 2020. "A Note on Some Bounds of the α‐Estrada Index of Graphs," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:3972789
    DOI: 10.1155/2020/3972789
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    References listed on IDEAS

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    1. Li, Jianxi & Guo, Ji-Ming & Shiu, Wai Chee & Altındağ, Ş. Burcu Bozkurt & Bozkurt, Durmuş, 2018. "Bounding the sum of powers of normalized Laplacian eigenvalues of a graph," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 82-92.
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