  We examine the possibility of a dark matter (DM) contribution to the recently
observed gamma-ray spectrum seen in the M31 galaxy. In particular, we apply
limits on Weakly Interacting Massive Particle DM annihilation cross-sections
derived from the Coma galaxy cluster and the Reticulum II dwarf galaxy to
determine the maximal flux contribution by DM annihilation to both the M31
gamma-ray spectrum and that of the Milky-Way galactic centre. We limit the
energy range between 1 and 12 GeV in M31 and galactic centre spectra due to the
limited range of former's data, as well as to encompass the high-energy
gamma-ray excess observed in the latter target. In so doing, we will make use
of Fermi-LAT data for all mentioned targets, as well as diffuse radio data for
the Coma cluster. The multi-target strategy using both Coma and Reticulum II to
derive cross-section limits, as well as multi-frequency data, ensures that our
results are robust against the various uncertainties inherent in modelling of
indirect DM emissions.
  Our results indicate that, when a Navarro-Frenk-White (or shallower) radial
density profile is assumed, severe constraints can be imposed upon the fraction
of the M31 and galactic centre spectra that can be accounted for by DM, with
the best limits arising from cross-section constraints from Coma radio data and
Reticulum II gamma-ray limits. These particular limits force all the studied
annihilation channels to contribute 1% or less to the total integrated
gamma-ray flux within both M31 and galactic centre targets. In contrast,
considerably more, 10-100%, of the flux can be attributed to DM when a
contracted Navarro-Frenk-White profile is assumed. This demonstrates how
sensitive DM contributions to gamma-ray emissions are to the possibility of
cored profiles in galaxies.
