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Topic: An Argument for the Subroot Node
Replies: 28   Last Post: Mar 14, 2008 8:32 PM

 Messages: [ Previous | Next ]
 J. Antonio Perez M. Posts: 2,736 Registered: 12/13/04
Re: An Argument for the Subroot Node
Posted: Mar 11, 2008 12:01 PM

On Mar 11, 5:51 pm, G. Frege <nomail@invalid> wrote:
> On Tue, 11 Mar 2008 08:40:29 -0700 (PDT), Tonico <Tonic...@yahoo.com>
> wrote:
>
>
>

> >> "In graph theory, a tree is a graph in which any two vertices are
> >>  connected by /exactly one/ path."

>
> > Where did you get that definition from?
>
> Wikipedia. Entry "Tree (graph theory)".
>
>
>

> > According to it, the perimeter of a triangle is a tree...
> > which, of course, it is not.

>
> Wait a second. If the nodes of your triangle were, say a, b, c then
> (say) a, b would be connected by more than one path:
>
>         p_1 = ((a,b), (b,c), (c,a))
>
>         p_2 = ((a,b), (b,c), (c,a), (a,b), (b,c), (c,a))
> [ or
>         p_3 = ((a,c), (c,b), (b,a)) ]
>
> See?
>

**********************************************************

Not really: in fact, I have no idea what you meant to denote by p_2.
When I talked of the perimeter of a triangle I meant a 2-simplex, or
the vertices-paths's graph denoted by, say p_1...I can't see how a
single pair of vertices would in this case be connected by more than
one path.

Regards
Tonio

Date Subject Author
3/11/08 Tony Orlow
3/11/08 Virgil
3/11/08 G. Frege
3/11/08 Tony Orlow
3/11/08 Virgil
3/11/08 Tony Orlow
3/11/08 Virgil
3/11/08 G. Frege
3/11/08 J. Antonio Perez M.
3/11/08 G. Frege
3/11/08 G. Frege
3/11/08 Tony Orlow
3/11/08 briggs@encompasserve.org
3/14/08 Tony Orlow
3/14/08 David R Tribble
3/14/08 LudovicoVan
3/11/08 Tony Orlow
3/11/08 J. Antonio Perez M.
3/11/08 Tony Orlow
3/11/08 Tony Orlow
3/11/08 Tony Orlow
3/11/08 LudovicoVan
3/11/08 LudovicoVan
3/14/08 Tony Orlow
3/14/08 LudovicoVan
3/14/08 LudovicoVan
3/11/08 David R Tribble
3/11/08 LudovicoVan
3/11/08 LudovicoVan