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

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David R Tribble

Posts: 3,426
Registered: 7/21/05
Re: An Argument for the Subroot Node
Posted: Mar 14, 2008 6:07 PM
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briggs wrote:
>> It seems fairly easy to prove that:
>>
>> 1. If a graph has a cycle, it will have two distinct nodes with
>> more than one path between them.
>>
>> 2. If a graph has two distinct nodes with more than one path between
>> them, it will contain a cycle.
>>
>> 3. If a graph is connected, there will be at least one path between
>> any pair of distinct nodes.
>>
>> 4. If a graph has at least one path between any pair of distinct nodes,
>> it is connected.

>

Tony Orlow wrote:
> Does this say anything about a node with a single edge between it and
> itself? It seems that doesn't quite qualify as a cycle, eh?


Of course it does. There is no need to explicitly mention
or rule out such edges because the rules implicitly do so
already.

A tree with a "root" node containing a path to itself would,
of course, have more than one path between it an any of
its children nodes, i.e., paths that go through the cyclical
link to itself and paths that don't, as per rule 1 above.


Date Subject Author
3/11/08
Read An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
Virgil
3/11/08
Read Re: An Argument for the Subroot Node
G. Frege
3/11/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
Virgil
3/11/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
Virgil
3/11/08
Read Re: An Argument for the Subroot Node
G. Frege
3/11/08
Read Re: An Argument for the Subroot Node
J. Antonio Perez M.
3/11/08
Read Re: An Argument for the Subroot Node
G. Frege
3/11/08
Read Re: An Argument for the Subroot Node
G. Frege
3/11/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
briggs@encompasserve.org
3/14/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/14/08
Read Re: An Argument for the Subroot Node
David R Tribble
3/14/08
Read Re: An Argument for the Subroot Node
LudovicoVan
3/11/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
J. Antonio Perez M.
3/11/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/11/08
Read Re: An Argument for the Subroot Node
LudovicoVan
3/11/08
Read Re: An Argument for the Subroot Node
LudovicoVan
3/14/08
Read Re: An Argument for the Subroot Node
Tony Orlow
3/14/08
Read Re: An Argument for the Subroot Node
LudovicoVan
3/14/08
Read Re: An Argument for the Subroot Node
LudovicoVan
3/11/08
Read Re: An Argument for the Subroot Node
David R Tribble
3/11/08
Read Re: An Argument for the Subroot Node
LudovicoVan
3/11/08
Read Re: An Argument for the Subroot Node
LudovicoVan

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