GRAPH INVARIANTS FOR FULLERENES

A comparison is made among several theoretical invariants in characterizing classes of fullerenes with up through 96 carbon atoms, namely all isomers of C-60, and all preferable higher fullerenes (i.e., fullerenes without abutting pentagons) with 60-96 carbon atoms. Four classes of fullerene structures were considered: first, the 1812 C-60 isomers; second, their duals; third, the 558 isolated-pentagon fullerenes with 60-96 carbon atoms; and fourth their duals. The invariants that were investigated are either purely graph-theoretical (including several topological indices, the number of Hamiltonian circuits, and the number of spanning trees), or associated with quantum-chemical interpretations (including Huckel pi-electron energy and HOMO-LUMO gap). In addition to such invariants that are expressed as a single numerical value (integer, rational, or real number), associations of several invariants have also been explored, such as the numbers of Kekule structures with those of conjugated circuits. Some of the above invariants succeeded in uniquely characterizing the studied fullerenes. This finding has implications for a rational coding and nomenclature of fullerenes.