The energy of some tree dendrimers

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.