On Wednesday, January 21, 2015 at 8:11:23 AM UTC-5, Nathann Cohen wrote:
>
> Hello,
>
> I'm looking at embeddings of complete gaphs and I think I've found a bug: 
>> I defined the complete graph k12 as a (sort of) Cayley graph of the group 
>> Z₂²× Z₃ as follows: 
>>
>
> First, it seems that the Python code you copy/pasted in your message lost 
> its indentation. Thus, I have no way to make sure that the identation I 
> used is the one that you used.
>
>
Sorry about that.  For what is worth here is the code with indentation:

 k12 = Graph()
for x in g12:
....for y in [A, B, A*B]:
........if not (x*y, x) in k12.edges():
............k12.add_edge((x, x*y))
....for y in [C, A*C, B*C, A*B*C]:
........k12.add_edge((x, x*y))

 the reset is all oneliners. 

This being said, it seems that the problem comes from your dictionary 
> 'imb': it should associated, to each vertex v of your graph, the list of 
> its neighbors in some cyclic ordering. What Sage seems to say, however, is 
> that while A*C appear in the list associated to 1, it is unable to find 1 
> in the list associated to A*C.
>
>

You're riight.  After looking carefully at my definition of cy (the cyclic 
order of the non zero group elements that give the cyclic order of the 
edges around each vertext) I noticed that instead of A*C^-1 I had AC^1. 
Once I corrected that everything works.

However shouldn't _check_embedding_validity detect that something was wrong 
with my dictionary? I did give 

k12._check_embedding_validity() 

and sage returned True. 

Anyway sorry for my silly mistake and thanks a lot for your help. 

Nikos 

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