Let G be a simple undirected graph. The energy E(G) of G is the sum of the absolute values of the eigenvalues of the adjacent matrix of G, and the Hosoya index Z (G) of G is the total number of matchings in G. A tree is called a nonconjugated tree if it contains no perfect matching. Recently, Ou ['Maximal Hosoya index and extremal acyclic molecular graphs without perfect matching', Appl. Math. Lett. 19 (2006), 652-656] determined the unique element which is maximal with respect to Z (G) among

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... e family of nonconjugated n-vertex trees in the case of even n. In this paper, we provide a counterexample to Ou's results. Then we determine the unique maximal element with respect to E(G) as well as Z (G) among the family of nonconjugated n-vertex trees for the case when n is even. As corollaries, we determine the maximal element with respect to E(G) as well as Z (G) among the family of nonconjugated chemical trees on n vertices, when n is even. 2000 Mathematics subject classification: primary 05C50; secondary 05C05, 05C35.