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Keywords

Estrada Indices; Perfect Matching; Trees

Abstract

Trees possessing no Kekul ́e structures (i.e., perfect matching) with the minimal Estrada index are considered. Let T_n be the set of the trees having no perfect matchings with n vertices. When n is odd and n ≥ 5, the trees with the smallest and the second smallest Estrada indices among T_n are obtained. When n is even and n ≥ 6, the tree with the smallest Estrada index in T_n is deduced.

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