Abstract

**Accepted 29 ^{th} June, 2015**

** **

**In this research paper, we compute the ranks and subdegrees of the symmetric group S _{n}(n = 3, 4, 5) acting on unordered pairs from the set X =**

**When S**

_{n }(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 S_{n}(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