Spectral Moments of Phenylenes

In a series of publications Estrada (Estrada, E. J. Chem. Inf. Comput. Sci. 1996, 36, 844-849; 1997 37, 320-328; 1998, 38, 23-27) employed spectral moments of line graphs in QSPR and QSAR relationship studies of various classes of compounds. A recent paper (Marković, S.; Gutman, I. J. Chem. Inf Comput. Sci. 1999, 39, 289-293) reported that in QSPR and QSAR investigations of benzenoid hydrocarbons based on linear combination of spectral moments, it made no difference whether one used spectral moments of the molecular graph or those of the line graph. In the present work spectral moments of molecular graphs (Mk) and line graphs (muk) of phenylenes are considered. The first few Mk's and muk'S of phenylenes are dependent on identical structural parameters. It is proved that the two sets of moments of phenylenes are linearly dependent. It is also shown that in the case of the heat of formation of phenylenes there is no advantage in using lower spectral moments of line graphs instead of lower spectral moments of molecular graphs. In this way the redundancy observed in the case of benzenoid hydrocarbons is also shown to exist in the class of phenylenes.