Spectral moments of the edge adjacency matrix in molecular graphs. Benzenoid hydrocarbons

The spectral moments of the edge adjacency matrix recently have been succes sfully employed in quantitative structure-properly relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies of alkanes, alk yl halides, benzyl alcohols, and cycloalkanes.(1-3) In this work we examine d spectral moments of the edge adjacency matrix of benzenoid hydrocarbons. We designed combinatorial formulas for spectral moments up to the seventh o rder. Our expressions depend on counts of certain structural features that can easily be deduced from the molecular graph. The first few spectral mome nts of the edge adjacency matrix and of the vertex adjacency matrix depend on the very same structural parameters, implying that the two sets of momen ts are equivalent from the vewpoint of QSPR and OSAR studies. We demonstrat e this for the total pi-electron energy.