Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs

Shang, Yilun (2020) Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs. Mathematics, 8 (7). p. 1063. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math8071063

Abstract

Let G be a simple graph of order n. The Estrada index and Laplacian Estrada index of G are defined by EE(G)=∑ni=1eλi(A(G)) and LEE(G)=∑ni=1eλi(L(G)) , where {λi(A(G))}ni=1 and {λi(L(G))}ni=1 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.

Item Type: Article
Uncontrolled Keywords: Estrada index; Laplacian Estrada index; eigenvalue; random graph
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 01 Jul 2020 13:17
Last Modified: 01 Jul 2020 13:30
URI: http://nrl.northumbria.ac.uk/id/eprint/43639

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