毛毛虫树的最大能量

摘要

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the adjacency matrix of the graph. A caterpillar tree is a tree in which removing the pendant vertices and incident edges. The energy of the graph is applied in chemistry to approximate the total π-electron energy of molecules. Ordering graphs by the energy is an important problem in chemical graph theory. In this paper, we discuss the energy of caterpillar trees and present the maximal energies of caterpillar trees and present the maximal energies of caterpillar trees with diameter no more than five by the quasi-ordering method.%图的能量定义为它的邻接矩阵的所有特征值绝对值之和，毛毛虫树是指去掉悬挂点和与其关联的悬挂边后只剩下一条路的树。在化学上，图的能量被用来近似分子的π电子总能量。依能量对图进行排序是化学图论中的一个重要研究课题。本文利用逆序的方法，对毛毛虫树能量进行了研究，给出了当毛毛虫树直径不超5时的最大能量树。