Symmetry, Vol. 7, Pages 2195-2205: Estrada Index of Random Bipartite Graphs

The Estrada index of a graph \(G\) of \(n\) vertices is defined by \(EE(G)=\sum_{i=1}^ne^{\lambda_i}\), where \(\lambda_1,\lambda_2,\cdots,\lambda_n\) are the eigenvalues of \(G\). In this paper, we give upper and lower bounds of \(EE(G)\) for almost all bipartite graphs by investigating the upper and lower bounds of the spectrum of random matrices. We also formulate an exact estimate of \(EE(G)\) for almost all balanced bipartite graphs.

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