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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?

Chill2Macht
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Yuxiao Xie
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  • To get you started, how many different alkanes are there with $n$ C atoms? – almagest May 21 '16 at 05:21
  • @almagest I've thought about that, but I don't know how to solve this. There are just so many isomorphic graphs when counting, and I don't know how to deal with this problem. – Yuxiao Xie May 21 '16 at 05:26
  • You might find this research abstract of interest, it starts by describing drug research that utilized combinatorics (and then goes on to talk almost exclusively about things called polyhexes, or polycyclic benzenoid hydrocarbons as they're known to chemists). It's mostly about polyhexes, but might yield a reference or two (that you'd have to track down yourself; none are listed). – pjs36 May 21 '16 at 05:27
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    Alkanes: http://oeis.org/A000602 might get you started. – almagest May 21 '16 at 05:35
  • @almagest The information there is overwhelming. Can you tell me about it? Are there any formulas or recurrence relations? – Yuxiao Xie May 21 '16 at 05:45
  • I think you are straying into a different question! – almagest May 21 '16 at 05:47
  • @almagest Yes, but I just want to try it out, as an example. – Yuxiao Xie May 21 '16 at 05:51
  • Yes, RDKit has modules dealing with graphs, the reaction mechanism generator RMG uses it. The keyword is Cheminformatics. – DetlevCM May 21 '16 at 10:20
  • You might be interested in"Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds" by Polya and Read: http://www.amazon.com/Combinatorial-Enumeration-Groups-Chemical-Compounds/dp/1461291054/ref=sr_1_1?ie=UTF8&qid=1463838724&sr=8-1&keywords=polya+chemical+compounds – awkward May 21 '16 at 13:54

1 Answers1

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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.

Chill2Macht
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