A series of trees with the first $\lfloor\frac{n-7}{2}\rfloor$ largest   energies
  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. 
Hai-Ying Shan, Jia-Yu Shao, Li Zhang, Chang-Xiang He
math.CO