Efficient Way for Factorizing the Characteristic Polynomial of Highly Symmetrical Graphs Such as the Buckminsterfullerene

Abstract

Abstract An efficient method is introduced for factoring out the characteristic polynomial of highly symmetrical graphs by using the highest rotational symmetry in the topological sense, even with the sacrifice of the higher 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 characteristic polynomial into the product of ten 6×6 determinants by noticing its topological symmetry of D10h. The mathematical structure of the highly degenerate Hückel molecular orbitals of C60 molecule was thus clarified. The C28 network was also analyzed.