树依能量的排序

Tree Ordering According to Minimal Energies

令Tn是顶点个数为n的树的集合.已有学者针对Tn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Tn中两个图能量的比较,另一个是Tn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Tn中当n≥7 117 599时前12个具有较小能量的树.

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