Bounds of the Estrada index of graphs

AbstractLet G be a graph of order n and let λ1, λ2, …, λn be its eigenvalues. The Estrada index [2] of G is defined as EE = EE(G) = $$ \sum\limits_{i = 1}^n {e^{\lambda _i } } $$. In this paper, new bounds for EE are established, as well as some relations between EE and graph energy E.