The isumers uf a given fullerene C„ cuuld be divided into subsets, each characterized by two numbers, p and q. The former denotes the number of bonds shared by two fused pentagons and the latter denotes the number of vertices being common to the triplets of pentagons. The HOMO-LUMO separation, Ax, and ir-electron energy per electron, EPE, have been studied from the graph-theoretical point of view. The dependence of Ax and EPE on p, q and n in fullerenes from C24 to Cgo is presented and discussed.