Estrada Indices; Perfect Matching; Trees
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.
Wang, Wen-Huan and Zhai, Chun-Xiang.
"Minimal Estrada index of the trees without perfect matchings",
Electronic Journal of Linear Algebra,
Volume 35, pp. 408-417.