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#### Keywords

Let $\mathcal{H}_{n}$ be the set of the trees having a perfect matching with $n$ vertices. The ordering of the trees in $\mathcal{H}_{n}$ according to their minimal Estrada indices is investigated. We obtain the trees with the smallest and the second smallest Estrada indices among $\mathcal{H}_{n}$ with $n\geq 6$.