Accepted 29th June, 2015


In this research paper, we compute the ranks and subdegrees of the symmetric group Sn(n = 3, 4, 5) acting on unordered pairs from the set X =  When Sn (n ≥ 4) acts on unordered pairs from X, the rank is 3.Therefore the main study will be on the subdegrees of the suborbitals. The suborbital graphs corresponding to the suborbitals of these actions are also constructed. The graph theoretic properties of these suborbital graphs are also discussed. When Sn (n ≥ 4) acts on unordered pairs the suborbital graphs  corresponding to the non-trivial suborbits  and , are connected, regular  complementary.


Keywords: Subdegrees, suborbital graphs of symmetric group, unordered pairs