  The energy of a graph is defined as the sum of the absolute values of the
eigenvalues of the graph. In this paper, we present a new method to compare the
energies of two $k$-subdivision bipartite graphs on some cut edges. As the
applications of this new method, we determine the first
$\lfloor\frac{n-7}{2}\rfloor$ largest energy trees of order $n$ for $n\ge 31$,
and we also give a simplified proof of the conjecture on the fourth maximal
energy tree.

Combinatorics