On the eigenvalues of molecular graphs

Hydrocarbon molecules, both conjugated and saturated, are conveniently characterized by their molecular graphs. Both physical and chemical properties have been directly related to graphical quantities. The eigenvalues of molecular graphs display many coincidences and regularities whose explanation is not immediate. It is shown that for alternants which possess a two-fold symmetry operation the eigenvalues must have certain relationships. These explain why certain eigenvalues occur frequently in the spectra of different molecules. Appropriate formulae are suggested for the largest eigenvalue and for the smallest positive eigenvalue (HOMO).