Estrada index of random bipartite graphs

Abstract

The Estrada index of a graph G of n vertices is defined by EE(G) = Σni=1 eλi, where λ1, λ2,.. λn 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.