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.