On the Study of the Substructure of Galaxy Clusters: S-Tree Technique in Non-Point Approximation

We represent the further development of S-tree technique of the study the structure of clusters of galaxies. The S-tree technique developed by Gurzadyan et al enables one to analyse the substructures of clusters via self-consistent use of 2D positional, 1D kinematical and magnitude information on the galaxies. First, the generalization of the method for the system of N-spheres, i.e. in non-point approximation, is performed, and the ways of construction of a new $D$ matrix are given. Second, an efficient algorithm for analyzing of the S-tree output information is presented, enabling one to reveal the existence of subgroups and the membership of galaxies in each subgroup.