Subdegrees and suborbital graphs of symmetric group s n (n = 3, 4, 5) acting on unordered pai rs

Abstract

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 the oretic 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 .