root vertex

root vertex

[′rüt ′vər‚teks]
(mathematics)
The vertex of a rooted tree that has no predecessor.
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Let us first consider the case of [x.sub.13] = 0, i.e., the root vertex [v.sub.13] of the tree is not installed with a facility.
A directed tree is a directed graph such that each vertex has only one parent vertex, except one special vertex (root vertex) without any parent vertex.
At each step, a root vertex is picked among the unaggregated vertices; then, an aggregate is formed with all the unaggregated vertices that have a path of length at most r to the root, where r is a given parameter.
As a consequence of Lemma 19, note that the root edge of every D gadget in any AB-graph G remains bad, that is, no matter whether other edges are incident to the root vertex r in G.
For generalization we introduce the following notations for a tree T with root vertex [v.sub.s].
Referring to the process of local modularity [18, 21], our algorithm selects the root vertex firstly and visits the adjacent nodes in next layer.
Let [T.sub.k] be an olive tree with branches [t.sub.1], [t.sub.2], ..., [t.sub.k], where k [greater than or equal to] 3 and let v be its root vertex. Then, [l.sub.v] = k and for all u [member of] V\{v}, [l.sub.u] = 1.
A directed tree is a directed graph where every vertex except the root vertex has exactly one parent vertex and the root vertex can be connected to any other vertices via paths.
Let T be a labelled tree with a root vertex [v.sub.[empty set]], labelled [empty set], the rest of the vertices labelled with the alphabet {[[x.sub.0], [x.sub.1], ...
Since each vertex (respectively, arc) in G can be attributed to one vertex (respectively, arc) in exactly one augmented graph, and there is one extra root vertex for each augmented graph, Expression (1) -- O(n + m).
We denote a monitored entity (ME) as [T.sub.v], where [T.sub.v] contains a root vertex v and any edge of G belongs to one and only one [T.sub.v].
In a tree with diameter D, no vertex is more than D/2 hops or edges from the root vertex of the tree [17].