  The possible presence of graphene in the interstellar medium (ISM) is
examined by comparing the interstellar extinction curve with the ultraviolet
absorption of graphene calculated from its dielectric functions experimentally
obtained with the electron energy loss spectroscopy (EELS) method. Based on the
absence in the interstellar extinction curve of the ~2755 Angstrom
$\pi$--$\pi^{\ast}$ electronic interband transition of graphene, we place an
upper limit of ~20ppm of C/H on the interstellar graphene abundance, exceeding
the previous estimate by a factor of ~3 which made use of the dielectric
functions measured with the spectroscopic ellipsometry (SE) method. Compared
with the SE method which measures graphene in air (and hence its surface is
contaminated) in a limited energy range of ~0.7--5 eV, the EELS probes a much
wider energy range of ~0--50 eV and is free of contamination. The fact that the
EELS dielectric functions are substantially smaller than that of SE naturally
explains why a higher upper limit on the graphene abundance is derived with
EELS. Inspired by the possible detection of C$_{24}$, a planar graphene sheet,
in several Galactic and extragalactic planetary nebulae, we also examine the
possible presence of C$_{24}$ in the diffuse ISM by comparing the model IR
emission of C$_{24}$ with the observed IR emission of the Galactic cirrus and
the diffuse ISM toward $l = 44^{o}20^\prime$ and $b=-0^{o}20^\prime$. An upper
limit of ~20 ppm on C$_{24}$ is also derived from the absence of the
characteristic vibrational bands of C$_{24}$ at ~6.6, 9.8 and 20 $\mu$m in the
observed IR emission.
