Characteristic polynomials and eigenvalues of molecular graphs with a greater than twofold axis of symmetry

Abstract

Molecular graphs with greater than a twofold axis of symmetry will possess at least one pair of identical eigenvalue subsets. Deletion of any atomic vertex or placement of a heteroatom or polyene substituent on any position of such a molecular graph, leads to a successor molecular graph still retaining one of these eigenvalue subsets. This graph theoretical property enabled the construction of a list of substructural units for recognizing the presence of select eigenvalues in molecules containing them.