The concept of energy of a graph was first introduced by I. Gutman [5] in 1978. The energy E(G) of a simple graph G is defined to be the sum of the absolute values of the eigenvalues of G. The tree dendrimer d(n, k) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in d(n, k) is connected to \((k-1)\). It is a rooted tree, with all other vertices arranged in shells around the root vertex, also called the central vertex. In this paper, the reduction formula for the characteristic polynomial of d(2, k) and d(3, k) is obtained. By using these reduction formulas, the energy of these graphs is also calculated. The comparison of energy for different values of n and k is also given.

的曲线图的能量的概念最早由I.古特曼[5]在1978年引入的能量 ë（ģ一个简单图的）ģ被定义为的本征值的绝对值的总和ģ。树状树状体d（n，  k）是一个有限连通的无循环图，也称为Bethe晶格。d（n，  k）中的每个顶点都连接到\（（k-1）\）。它是一棵有根的树，所有其他顶点围绕着根顶点（也称为中心顶点）排列在壳中。本文针对d的特征多项式的约简公式得到（2，  k）和d（3，  k）。通过使用这些归约公式，还可以计算这些图的能量。还给出了n和k不同值的能量比较。