Intersection matrices associated with non trivial suborbit corresponding to the action of rank 3 groups on the set of unordered pairs

Abstract

In this paper we find intersection numbers and intersection matrices associated with each non trivial sub orbit corresponding to the action of rank 3 groups; The symmetric group S5,alternating group A5 and The dihedral group D5 on the set of unordered pairs. We showed that the column sum of the intersection matrices associated with i is equal the length of the suborbit i . They are also square matrices and of order 3x3.