Derivation of Cycle Index Formulas for Dihedral Group Acting on Unordered Triples

The cycle index of dihedral group D_n acting on the set X of the vertices of a regular n-gon was studied by Harary and Palmer in 1973 (See [1]). In this paper we derive the cycle index formulas of the dihedral group (D_n) acting on unordered triples from the set X={1, 2, , n}. In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of n and an odd value of n.