Cycle Index Formulas for Dn Acting on Unordered Pairs

The concept of the cycle index was discovered by Polya (See [2]) and he gave it its present name. He used the cycle index to count graphs and chemical compounds via the Polya’s Enumeration Theorem. More current cycle index formulas include the cycle index of the reduced ordered triples groups (See [3]) which was further extended by Kamuti and Njuguna to cycle index of the reduced ordered r-group (See [4]). The Cycle Index of Internal Direct Product Groups was done in 2012 (See [5]).