Tenth Spectral Moment for Molecular Graphs of Phenylenes

Our investigations are motivated by recent papers concerning the spectral moments of the edge-adjacency matrix, which were successfully employed in QSAR and QSPR studies of different classes of compounds [Estrada, E. J. Chem. Inf. Comput. Sci. 1996, 36, 844-849; 1997, 37, 320-328; 1998, 38, 23-27]. In this work, the evaluation of the 10th spectral moment of the vertex-adjacency matrix for phenylenes is considered. This is achieved by using the method of Hall [Hall, G. G. Theor. Chim. Acta 1986, 70, 323-332], which was originally applied to benzenoid systems and then adopted for molecular graphs of phenylenes [Marković, S.; Stajković, A. Theor. Chem. Acc. 1997, 96, 256-260]. It is found that the 10th spectral moment can be expressed in terms of 6 mutually independent invariants that can be easily deduced from the molecular graph.