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

 Messages: [ Previous | Next ]
 Tony Orlow Posts: 3,142 Registered: 8/23/06
Re: An Argument for the Subroot Node
Posted: Mar 11, 2008 1:26 PM

Tonico wrote:
> 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

In triangle abc, vertices a and b are connected by two simple paths,
((a,b)) and ((a,c),(c,b)).

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