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.


1 Answer 1


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



for examples

  • $\begingroup$ Ok, but what about condition 3? $\endgroup$ Commented May 5, 2017 at 5:03
  • $\begingroup$ Sure, I've updated my answer $\endgroup$
    – ManRow
    Commented May 5, 2017 at 5:45

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