On the Energy of Benzenoid Hydrocarbons

In chemistry, the energy of a graph is of interest since it can be used to approximate the total pi-electron energy of molecules. The spectral moments of the edge adjacency matrix and adjacency matrix recently have been successfully employed in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies of alkanes, alkyl halides, benzyl alcohols, cycloalkanes, and benzenoid hydrocarbons. Let G be a molecular graph and L(G) be a line graph, then the eigenvalues of G and L(G) are denoted by, lambda(1) >= lambda(2) >= ... >= lambda(n) and gamma(1) >= gamma(2) >= ... >= gamma(n), respectively. The energies A and L(G) are defined as epsilon(G)= Sigma(n)(i=1)|lambda(i)| and epsilon(L(G))= Sigma(n)(i=1)|gamma(i)|. In this paper, we examined both energies with spectral moments of the edge adjacency matrix and adjacency matrix of benzenoid hydrocarbons. These theoretical conclusions provide practical guiding significance for pharmaceutical engineering, complex network and quantify the degree of folding of long organic molecules.