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On the Estrada Indices of Unicyclic Graphs with Fixed Diameters

Author

Listed:
  • Wenjie Ning

    (College of Science, China University of Petroleum (East China), Qingdao 266580, China)

  • Kun Wang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

The Estrada index of a graph G is defined as E E ( G ) = ∑ i = 1 n e λ i , where λ 1 , λ 2 , … , λ n are the eigenvalues of the adjacency matrix of G . A unicyclic graph is a connected graph with a unique cycle. Let U ( n , d ) be the set of all unicyclic graphs with n vertices and diameter d . In this paper, we give some transformations which can be used to compare the Estrada indices of two graphs. Using these transformations, we determine the graphs with the maximum Estrada indices among U ( n , d ) . We characterize two candidate graphs with the maximum Estrada index if d is odd and three candidate graphs with the maximum Estrada index if d is even.

Suggested Citation

  • Wenjie Ning & Kun Wang, 2021. "On the Estrada Indices of Unicyclic Graphs with Fixed Diameters," Mathematics, MDPI, vol. 9(19), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2395-:d:643447
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    References listed on IDEAS

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    1. Sun, Qiang & Ikica, Barbara & Škrekovski, Riste & Vukašinović, Vida, 2019. "Graphs with a given diameter that maximise the Wiener index," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 438-448.
    2. Liu, Chang & Pan, Yingui & Li, Jianping, 2021. "On the geometric-arithmetic Estrada index of graphs," Applied Mathematics and Computation, Elsevier, vol. 391(C).
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