The morphology of clusters of galaxies may be described with a set of parameters which contain information about the formation and evolutionary history of these systems. In this paper we present a preliminary study of the morphological parameters of a sample of 28 compact Abell clusters extracted from DPOSS data. The morphology of galaxy clusters is parameterized by their apparent ellipticity, position angle of the major axis, centre coordinates, core radius and beta-model power law index. Our procedure provides estimates of these parameters by simultaneously fitting them all, overcoming some of the difficulties induced by sparse data and low number statistics typical of this kind of analysis. The cluster parameters were fitted in a 3 x 3 h^-2 sqMpc region, measuring the background in a 2 <R< 2.5 h^-1Mpc annulus. We also explore the correlations between shape and profile parameters and other cluster properties. One third of this compact cluster sample has core radii smaller than 50 h^-1 kpc, i.e. near the limit that our data allow us to resolve, possibly consistent with cusped models. The remaining clusters span a broad range of core radii up to 750 h^-1 kpc. More than 80 per cent of this sample has ellipticity higher than 0.2. The alignment between the cluster and the major axis of the dominant galaxy is confirmed, while no correlation is observed with other bright cluster members. No significant correlation is found between cluster richness and ellipticity. Instead, cluster richness is found to correlate, albeit with large scatter, with the cluster core radius.[abridged]
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