令T_n是顶点个数为n的树的集合.已有学者针对T_n中树依能量从小到大的排序提出了两个猜想,其中一个猜想是T_n中两个图能量的比较，另一个是T_n中当n≥7 117 599时的第10小至第12小能量树.该文证明这两个猜想成立；确定T_n中当n≥7 117 599时前12个具有较小能量的树.

Let T_n be a set of trees with n vertices. The increasing orders in terms of the minimal energies of the trees in T_n had been considered and two conjectures were proposed. The first one is the comparison of the energies of two graphs in T_n. The other is about the trees with the 10th to 12th minimal energies for n≥7 117 599. This paper proves that the two conjectures are true, and obtain the first 12 trees within T_n for n≥7 117 599.