A Graph-Theoretical Study of Conjugated Systems Containing a Linear Polyene Fragment

Conjugated molecules containing a linear polyene fragment are studied using graph theory. It is shown that the characteristic polynomials of the molecular graphs of .these sy&tems fulfill a common recurrence relation and have, therefore, a common general form. The spectra of 10 classes of isuch graphs are obtained in analytical form. These spectra are mutually related and are also related to the spectrum of cycles (which are molecular graphs of annulenes). From the spectra obtaililed analytical expressions for total n:-electron energy, HOMO-LUMO separation, etc. are deduced