# Re: dual graph

From: Dmitry A. Kazakov <mailbox_at_dmitry-kazakov.de>
Date: Tue, 27 Jun 2006 09:16:14 +0200
Message-ID: <7fngvin8f2no.wbi23fndg7aq\$.dlg_at_40tude.net>

On Mon, 26 Jun 2006 13:33:51 -0600, Chris Smith wrote:

> You've really lost me now. The question was what to call a graph whose
> dual has only one node (i.e., the edges don't divide the plane). The
> correct answer is "forest" (or "tree", if we assume connectedness).
> "Ordered" is decidedly not a correct answer.

OK, I thought the question was about hierarchies. My mistake.

```>>> Any graph
>>> (planar or not, cycles or not, doesn't matter) may be made into an
>>> ordered graph simply by defining an order for its nodes.
>>
>> If you can order the set of nodes. But that order is not necessary G*.
```

>
> Of course I can order the set of nodes. I just start somewhere, and
> start counting, like so... 1, 2, 3, 4, and so on.
> Who cares if the
> order I come up with is equivalent to the transitive closure of a
> directed graph?

The hierarchy does.

```--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
```
Received on Tue Jun 27 2006 - 09:16:14 CEST

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