Application of Combinatorics/Graph Theory to Organic Chemistry?

Question

Recently, I have been self-teaching graph theory and having an organic chemistry course at school.

When I was learning isomer enumeration I found great resemblance between organic molecules and graphs. Every atom can be regarded as a vertex, with carbon vertices of $4$ degree, hydrogen atoms of $1$ degree etc. On the whole they just constitute a loopless yet usually not simple graph!

While I am excited about this idea, I am unclear about how to apply graph theory (and some combinatorial techniques) to chemistry.

Am I correct? Are there really applications of combinatorics or graph theory to organic chemistry, particularly isomer enumeration? If so how? Are there any books or resources from where I can learn about this amazing idea?

Answer 1

Yes there are quite a lot actually, see for example Trinajstic's book Chemical Graph Theory.

http://docdro.id/L3DrG6B
or
https://www.scribd.com/doc/313337501/Chemical-Graph-Theory-Trinajstic

To list some of the topics discussed in the book verbatim, we have for example:

• Kekule structures
• Hückel theory
• the conjugated circuit model
• Zagreb group
• Cayley generating function for enumerating isomers

Actually most (if not all) applications in that book seem to be exclusively for organic chemistry, so you have quite a lot to choose from.