General features of the polyene references graph-theoretically defined for fullerenes

A matching polynomial has been used as a characteristic polynomial for the aromaticity-free polyene reference of a fullerene molecule. All π-electron molecular orbitals (π-MOs) in the polyene references of all fullerene isomers with a given number of carbon atoms were plotted on a single energy scale. The quasi-density-of-state (DOS) curve thus obtained for the polyene references is totally different in appearance from that for the actual fullerene isomers. The quasi-DOS curve for the polyene references exhibits little individuality, in the sense that all peaks in it are distributed with near-equal energy separations.