Estrada index of dynamic random graphs

Abstract

The Estrada index of a graph G on n vertices is defined by \(EE(G) = \sum\nolimits_{i = 1}^n {{e^{{\lambda _i}}}} \), where λ₁, λ₂, ⋯, λ_n are the adjacency eigenvalues of G. We define two general types of dynamic graphs evolving according to continuous-time Markov processes with their stationary distributions matching the Erdös-Rényi random graph and the random graph with given expected degrees, respectively. We formulate some new estimates and upper and lower bounds for the Estrada indices of these dynamic graphs.