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Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs

Author

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  • Yilun Shang

    (Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK)

Abstract

Let G be a simple graph of order n . The Estrada index and Laplacian Estrada index of G are defined by E E ( G ) = ∑ i = 1 n e λ i ( A ( G ) ) and L E E ( G ) = ∑ i = 1 n e λ i ( L ( G ) ) , where { λ i ( A ( G ) ) } i = 1 n and { λ i ( L ( G ) ) } i = 1 n are the eigenvalues of its adjacency and Laplacian matrices, respectively. In this paper, we establish almost sure upper bounds and lower bounds for random interdependent graph model, which is fairly general encompassing Erdös-Rényi random graph, random multipartite graph, and even stochastic block model. Our results unravel the non-triviality of interdependent edges between different constituting subgraphs in spectral property of interdependent graphs.

Suggested Citation

  • Yilun Shang, 2020. "Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs," Mathematics, MDPI, vol. 8(7), pages 1-8, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1063-:d:379031
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    References listed on IDEAS

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    1. Shang, Yilun, 2015. "The Estrada index of evolving graphs," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 415-423.
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    Cited by:

    1. Maryam Baghipur & Modjtaba Ghorbani & Hilal A. Ganie & Yilun Shang, 2021. "On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue," Mathematics, MDPI, vol. 9(5), pages 1-12, March.

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