Polya's Enumeration Theorem : Number of colorings of n-gons and non isomorphic graphs,

Polya’s theorem can be used to enumerate objects under permutation groups. Using grouptheory, combinatorics and some examples, Polya’s theorem and Burnside’s lemma arederived. The examples used are a square, pentagon, hexagon and heptagon under theirrespective dihedral groups. Generalization using more permutations and applications tograph theory.Using Polya’s Enumeration theorem, Harary and Palmer [5] give a function whichgives the number of unlabeled graphs n vertices and m edges. We present their work andthe necessary background knowledge