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Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs

Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
Mathematics 2020, 8(7), 1063; https://doi.org/10.3390/math8071063
Received: 8 June 2020 / Revised: 28 June 2020 / Accepted: 29 June 2020 / Published: 1 July 2020
(This article belongs to the Special Issue Algebra and Its Applications)
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. View Full-Text
Keywords: Estrada index; Laplacian Estrada index; eigenvalue; random graph Estrada index; Laplacian Estrada index; eigenvalue; random graph
MDPI and ACS Style

Shang, Y. Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs. Mathematics 2020, 8, 1063.

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