Application of Polya's Theorem to some special compounds of chemical graph theory

Abstract

Polya’s Enumeration Theorem uses polynomials to count isomers for many chemical compounds. The coefficients of the polynomials give the corresponding number of isomers. The exponent of each term gives the number of monovalent atoms. In this thesis, we present some examples to show how to apply Polya’s Theorem to some chemical compounds. Examples are given of some chemical compounds to which Polya’s Theorem is not applicable. Also, we show how Burnside’s Lemma can be applied when Polya’s Theorem fails. This thesis research proposes to study and answers the following questions: (1) How many total bromine isomers of cyclobutadiene C₄H_4-xBr _x exist? (2) How many total methyl isomers of Pyrrole C₄H_5-x N(CH₃)_x Exist? (3) And does Polya’s Theorem work if there are no isomers NH ₃?