Counting Chemical Isomers with Multivariate Generating Functions

TL;DR

This paper introduces multivariate generating functions to count complex chemical isomers, extending graph theory methods to more chemically realistic classes of molecules.

Contribution

It develops new counting techniques for chemically complex molecules using multivariate generating functions, bridging graph theory and network science.

Findings

Derived results for two new classes of molecules with chemical complexity

Demonstrated the use of multivariate generating functions in chemical counting problems

Highlighted the importance of counting theory in network science

Abstract

Counting the number of isomers of a chemical molecule is one of the formative problems of graph theory. However, recent progress has been slow, and the problem has largely been ignored in modern network science. Here we provide an introduction to the mathematics of counting network structures and then use it to derive results for two new classes of molecules. In contrast to previously studied examples, these classes take additional chemical complexity into account and thus require the use of multi-variate generating functions. The results illustrate the elegance of counting theory, highlighting it as an important tool that should receive more attention in network science.