  We present new limits on the graviton mass using a sample of 12 relaxed
galaxy clusters, for which temperature and gas density profiles were derived by
Vikhlinin et al (astro-ph/0507092) using Chandra X-ray observations. These
limits can be converted to a bound on the graviton mass, assuming a non-zero
graviton mass would lead to a Yukawa potential at these scales. For this
purpose, we first calculate the total dynamical mass from the hydrostatic
equilibrium equation in Yukawa gravity and then compare it with the
corresponding mass in Newtonian gravity. We calculate a 90 % c.l. lower/upper
limit on the graviton Compton wavelength/ mass for each of the 12 clusters in
the sample. The best limit is obtained for Abell 2390, corresponding to
$\lambda_g > 3.58\times 10^{19}$ km or $m_g<3.46 \times 10^{-29}$ eV. This is
the first proof of principles demonstration of setting a limit on the graviton
mass using a sample of related galaxy clusters with X-ray measurements and can
be easily applied to upcoming X-ray surveys such as eRosita.
