Isomorphism classes of bipartite cycle permutation graphs

Abstract

In this paper, we count the number of isomorphism classes of bipartite n-cyclic permutation graphs up to positive natural isomorphism and show that it is equal to the number of double cosets of the dihedral group D-n in the subgroup B-n of the symmetric group S-n consisting of parity-preserving or parity-reversing permutations.