Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. Benzenoid Hydrocarbons

The spectral moments of the edge 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, and cycloalkanes.1-3 In this work we examined spectral moments of the edge adjacency matrix of benzenoid hydrocarbons. We designed combinatorial formulas for spectral moments up to the seventh order. Our expressions depend on counts of certain structural features that can easily be deduced from the molecular graph. The first few spectral moments of the edge adjacency matrix and of the vertex adjacency matrix depend on the very same structural parameters, implying that the two sets of moments are equivalent from the vewpoint of QSPR and QSAR studies. We demonstrate this for the total π-electron energy.