For a graph G of n vertices, let λ_1, λ_2,···,λ_n be the eigenvalues of itsadjacency matrix. The Estrada index of G is defined by EE(G) =n∑i=1e~(λ_i).In this paper, we give some new lower and upper bounds for EE of bipartitegraphs. We determine the first three trees with the greatest Estrada index.
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