Application of Combinatorics/Graph Theory to Organic Chemistry? 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?

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

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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.