A topological index is a kind of molecular descriptor which anticipates some properties of chemical compound. The aim of this paper is to compute the spectrum of PA adjacency matrix associated to a well-known topological index.

The concept of energy of graph is defined in 1978 by Ivan Gutman as the sum of the absolute values of the eigenvalues of a graph. In this article we estimate the energy of small fullerenes.

Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The augmented eccentric connectivity index of graph G is defined as £(G)=∑u εV(G)M(u)ε(u)