EFFICIENT WAY FOR FACTORIZING THE CHARACTERISTIC POLYNOMIAL OF HIGHLYSYMMETRICAL GRAPHS SUCH AS THE BUCKMINSTERFULLERENE

An efficient method is introduced for factoring out the characteristic polynomial of highly symmetrical graphs by using the highest rotation al symmetry in the topological sense, even with the sacrifice of the h igher symmetry elements in the geometrical structure. The approach is demonstrated for the graph of the buckminsterfullerene of eicosahedral geometrical symmetry, where one can efficiently factor out its charac teristic polynomial into the product of ten 6x6 determinants by notici ng its topological symmetry of D-10h. The mathematical structure of th e highly degenerate Huckel molecular orbitals of C-60 molecule was thu s clarified. The C-28 network was also analyzed.