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Re: [ontolog-forum] What words mean

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Wacek Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Date: Sat, 23 Feb 2008 16:19:43 +0100
Message-id: <47C0398F.2050502@xxxxxxxxxxx>
Azamat wrote:
> Paola,
> By a strict definition, tree (diagram) is a plane figure that branches 
> from a single root, what makes a graphic way to represent any 
> hierarchical structure. Created as the mixed metaphors after family 
> relationships (parent/child), graph theory (node), and botanic 
> notions, the tree vocabulary is marked by the root nodes (superior, 
> ancestor), internal nodes (parent/child), leaf nodes (child); subtrees 
> and forest, a set of rooted trees. 
>     ----- Original Message -----
>     *From:* paola.dimaio@xxxxxxxxx <mailto:paola.dimaio@xxxxxxxxx>
>     *To:* [ontolog-forum] <mailto:ontolog-forum@xxxxxxxxxxxxxxxx>
>     *Sent:* Friday, February 22, 2008 8:23 PM
>     *Subject:* Re: [ontolog-forum] What words mean
>     Christopher and all
>     is there a rule or other guideline to prescribe when a tree should
>     have one, and when more than one root?
In what sense of 'should' should a tree have one or more roots?  What 
sort of context (pardon) do you mean here as the source of demand for 
one or more roots?    (01)

By definition (one from graph theory, Azamat might have had other 
definitions in mind), a tree is a connected acyclic graph.  Undirected 
trees have no roots.    (02)

A rooted tree is a directed tree with exactly one distinguished vertex 
chosen as the tree's root.  Following the definition (in a rooted tree, 
there is exactly one path from the root to any other vertex in the 
graph), if a tree were to have two roots, each of them would have to be 
accessible from the other, which implies a cycle in the graph;  but such 
a graph is not a tree.    (03)

vQ    (04)

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