On Some Graphs Associated with Permutations

Abstract

A permutation on the set X = {1, 2, ... , n} is a bijective function from X to itself. The set of all permutations on X is called the symmetric group and is denoted by Sym(n). An m-cyclic permutation is a permutation which moves m elements of X "cycle-wise" and does not move the other elements. For any 2<=m<=n define the graph "Gamma(n,m)" to be the graph whose vertices are all the elements of Sym(n) and two vertices are adjacent if one of them is equal to the composition of the other one with an m-cyclic permutation. In this talk we study the maximum independent sets of these graphs.