SUBORBITAL GRAPHS OF THE SYMMETRIC GROUP Sn ACTING ON UNORDERED r-ELEMENT SUBSETS

Abstract

In this paper we construct the suborbital graphs of the symmetric group Sn acting on  unordered r‐element subsets of X = {1, 2, 3,  ..., n}, X(r)(,∈ℕ) and  analyse their properties. It is shown that the suborbital graphs are undirected, connected if <  , and have girth three if  n ≥ 3r