How can I define alkenes using graph theory? I want to represent alkenes in a mathematical fashion but I want to make sure of what I'm writing. Here is what I tried by defining "alkenic" graphs:

Alkenic graphs are connected non-looped multigraphs where:


nodes are of degree less than 5 (octet rule);
there is at least a double edge and no triple or quadruple ones (edges like in bonds);
cyclic submultigraphs with conjugated single-double edges given in any conjugation order are to be considered isomorphic (anti aromatic or aromatic isomorphism).
For example, the graphs representing "1,4-dimethylcyclobuta-1,3-diene" and "1,2-dimethylcyclobuta-1,3-diene" are isomorphic.


In this case I'm not taking stereoisomers into account.
Perhaps you could just represent them as simple weighted graphs? Edges of weight 1 represent single bonds, while edges of weight 2 represent double-bonds.

*Edit: For condition #3 simply pick a canonical ordering for the vertices/atoms. See 

https://en.m.wikipedia.org/wiki/Graph_canonization 

http://depth-first.com/articles/2006/08/12/inchi-canonicalization-algorithm/ 

for examples