Abstract
Graph energy is an invariant that is derived from the spectrum of the adjacency matrix of a graph. Graph energy is actually the absolute sum of all the eigenvalues of the adjacency matrix of a graph i.e. E= n-ary sumation(i=1)(n)lambda(i), and the Estrada index of a graph G is elaborated as EEG= n-ary sumation(i=1)(n)e(lambda i), where, lambda(1), lambda(2), horizontal ellipsis , lambda(n) are the eigenvalues of the adjacency matrix of a graph. In this paper, energy EG and Estrada index EEG of different molecular structures are obtained and also established inequalities among the exact and estimated values of energies and Estrada index of TUC4C8 nanosheet and naphthalene.