  Certain dust particles in space are expected to appear as clusters of
individual grains. The morphology of these clusters could be fractal or
compact. In this paper we study the light scattering by compact and fractal
polycrystalline graphitic clusters consisting of touching identical spheres. We
compare three general methods for computing the extinction of the clusters in
the wavelength range 0.1 - 100 micron, namely, a rigorous solution (Gerardy &
Ausloos 1982) and two different discrete-dipole approximation methods --
MarCODES (Markel 1998) and DDSCAT (Draine & Flatau 1994). We consider clusters
of N = 4, 7, 8, 27,32, 49, 108 and 343 particles of radii either 10 nm or 50
nm, arranged in three different geometries: open fractal (dimension D = 1.77),
simple cubic and face-centred cubic. The rigorous solution shows that the
extinction of the fractal clusters, with N < 50 and particle radii 10 nm,
displays a peak within 2% of the location of the observed interstellar
extinction peak at ~4.6 inverse micron; the smaller the cluster, the closer its
peak gets to this value. By contrast, the peak in the extinction of the more
compact clusters lie more than 4% from 4.6 inverse micron. At short wavelengths
(0.1 - 0.5 micron), all the methods show that fractal clusters have markedly
different extinction from those of non-fractal clusters. At wavelengths > 5
micron, the rigorous solution indicates that the extinction from fractal and
compact clusters are of the same order of magnitude. It was only possible to
compute fully converged results of the rigorous solution for the smaller
clusters, due to computational limitations, however, we find that both
discrete-dipole approximation methods overestimate the computed extinction of
the smaller fractal clusters.
