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The energy of a graph is defined as the sum of the absolute values of theeigenvalues of the graph. In this paper, we present a new method to compare theenergies of two $k$-subdivision bipartite graphs on some cut edges. As theapplications 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 maximalenergy tree.

A series of trees with the first $\lfloor\frac{n-7}{2}\rfloor$ largest energies