  Several planetary nebulae (PNe) have been found to contain both polycyclic
aromatic hydrocarbon (PAH-like) species and fullerenes (C$_{60}$) distinguished
by their mid-infrared emission. Previous laboratory and astronomical studies
suggest that the formation of both species could be related to the
decomposition, by photochemical processing, of hydrogenated amorphous carbon
(HAC) grains. Then, HACs and, seemingly, big-fullerene related species (e.g.,
carbon onions) have been suggested as potential carriers of the UV bump at
2175{\AA} and the far-UV rise common to interstellar extinction curves. Our
goal is to investigate the UV bump with the possible presence of a HAC
extinction component in the International Ultraviolet Explorer (IUE) spectra of
C-rich PNe; both with detected and non-detected fullerenes. The considered
sample includes three C$_{60}$-PNe (Tc 1, IC 418, and IC 2501) and the
non-C$_{60}$-PN Hen 2-5. Independently of the presence of C$_{60}$ in their
circumstellar envelopes, we found that the UV bump in all sample PNe is well
explained by interstellar extinction, suggesting that species different from
those of the foreground insterstellar medium, e.g., large fullerene-related
species like carbon onions, are not the carrier. Interestingly, we found that
PNe Tc 1 and Hen 2-5 show an absorption in the FUV rise. Their IUE continuum
spectra may be very well reproduced by including the extinction curve of
HAC-like very small grains (VSG). The possible presence of both species,
HAC-like grains and fullerenes (C$_{60}$), in Tc 1 could support the HAC
photochemical processing scenario for the formation of fullerenes in the
complex circumstellar envelopes of PNe.
