TITLE: Application of Combinatorics/Graph Theory to Organic Chemistry?
QUESTION [9 upvotes]: 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?

REPLY [8 votes]: 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.