  The classification of galaxy clusters according to their X-ray appearance is
a powerful tool to discriminate between regular clusters (associated to relaxed
objects) and disturbed ones (linked to dynamically active systems). The
compilation of the two subsamples is a necessary step both for cosmological
studies - oriented towards spherical and virialized systems- and for
astrophysical investigations - focused on phenomena typically present in highly
disturbed clusters such as turbulence, particle re-acceleration,
magneto-astrophysics . In this paper, we review several morphological
parameters: asymmetry and fluctuation of the X-ray surface brightness, hardness
ratios, X-ray surface-brightness concentration, centroid shift, and third-order
power ratio. We test them against 60 Chandra-like images obtained from
hydrodynamical simulations through the X-ray Map Simulator and visually
classified as regular and disturbed. The best performances are registered when
the parameters are computed using the largest possible region (either within
R500 or 1000 kpc). The best indicators are the third-order power ratio, the
asymmetry parameter, and the X-ray-surface-brightness concentration. All their
combinations offer an efficient way to distinguish between the two
morphological classes achieving values of purity extremely close to 1. A new
parameter, M, is defined. It combines the strengths of the aforementioned
indicators and, therefore, resulted to be the most effective parameter
analyzed.
