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My objective is to enumerate hydrocarbons as 3d structures and I want to take stereoisomers into account. Is there already a mathematical way to count and describe those objects? I started by using a topological approach.

A hydrocarbon is a connected (non looped according to some authors) multigraph where every node is a carbon with degree less than 5 (octet rule) and each is connected to 4 minus its degree hydrogens. My problem is that I don't know how to describe spatial orientations in a graph like that. I was thinking of a three-dimensional realization of such a graph so that stereoisomers would become distinguishable.

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    That kind of graph is designed to abstract away chirality and other such spatial properties. But there's a physical reason why left-handed isomers don't spontaneously mutate into right-handed isomers and back again (at least, I suppose they don't), so perhaps you can represent that somehow. – 2017-02-02
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    You should provide graphical representations (or give www references) for such a geometrical question. – 2017-02-02
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    Do you know the amazing library called Combinatorica (under Mathematica) (http://reference.wolfram.com/language/Combinatorica/tutorial/Combinatorica.html) ? – 2017-02-02
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    You could start with this answer on chemistry : http://chemistry.stackexchange.com/a/40911 – 2017-02-02
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    You might be interested in Polya's Enumeration Theorem. Historically, it has been used to enumerate chemical compounds. https://en.wikipedia.org/wiki/P%C3%B3lya_enumeration_theorem – 2017-02-02

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