The energy E(C) of a graph G is defined as the sum of the absolute values of eigenvalues of G and the Hosoya index of a graph G is defined as the number of matchings of G. Let Tn be the set of trees of order n≥ 4 with at least [n+2/2] pendant vertices. We characterize the tree with the maximal energy or Hosoya index in Tn. As an application of our result, we obtain a new method to prove a result obtained by Brualdi (Discrete Math., 48(1984), 1-21).
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