  Over the past decade, studies of dust in the Andromeda galaxy (M31) have
shown radial variations in the dust emissivity index ($\beta$). Understanding
the astrophysical reasons behind these radial variations may give clues about
the chemical composition of dust grains, their physical structure, and the
evolution of dust. We use $^{12}$CO(J=1-0) observations taken by the Combined
Array for Research in Millimeter Astronomy (CARMA) and dust maps derived from
\textit{Herschel} images, both with an angular resolution of 8" and spatial
resolution of 30 pc, to study variations in $\beta$ across an area of $\approx$
18.6 kpc$^2$ in M31. We extract sources, which we identify as molecular clouds,
by applying the astrodendro algorithm to the $^{12}$CO and dust maps, which as
a byproduct allows us to compare continuum emission from dust and CO emission
as alternative ways of finding molecular clouds. We then use these catalogues
to investigate whether there is evidence that $\beta$ is different inside and
outside molecular clouds. Our results confirm the radial variations of $\beta$
seen in previous studies. However, we find little difference between the
average $\beta$ inside molecular clouds compared to outside molecular clouds,
in disagreement with models which predict an increase of $\beta$ in dense
environments. Finally, we find some clouds traced by dust with very little CO
which may be either clouds dominated by atomic gas or clouds of molecular gas
that contain little CO.
