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I was, and still am, out seeking a way to get the adjacency matrix of the dual of $G$ without pen and paper. hardmath answered that the way I posted the question, it doesn't have a unique dual graph and it's therefore not possible to construct the adjacency matrix. But he also gave me useful information about how to fix the question to get an answer to my question.

Now I have two options:

  1. Edit the question, but this would make hardmath's answer look a little strange.
  2. Repost another question with the additional $3$-connectedness condition, which would be close to a duplicate to the one linked above.

So, both don't perfectly fit. I found this "edit and rephrase or ask new question?" on meta, but the answers don't fit to my case. What to do?

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    $\begingroup$ You should re-post the new question with a link to the old one, and an explanation of why you are posting it (that is, how the two questions differ). (I am pretty sure this has come up before, but I cannot find an example.) $\endgroup$ – user1729 Aug 4 '13 at 20:24
  • $\begingroup$ @user1729 thanks, done. Please flag this question as duplicate when you find the corresponding one... $\endgroup$ – draks ... Aug 4 '13 at 21:30
  • $\begingroup$ @user1729: maybe this one? $\endgroup$ – Willie Wong Aug 5 '13 at 7:35
  • $\begingroup$ @WillieWong I am sure that there is a closer match somewhere. The best I can find so far is Aryabhata's comment to Arturo Magidin answer to this (related) question. $\endgroup$ – user1729 Aug 5 '13 at 8:49
  • $\begingroup$ I think this question is the closest. I have flagged it as a duplicate. (Interestingly, it is Aryabhata who provides the answer!) $\endgroup$ – user1729 Aug 5 '13 at 8:57