# isolated vertex

## isolated vertex

[¦ī·sə‚lād·əd ′vər‚teks]
(mathematics)
A vertex of a graph that has no edges incident to it.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Add an isolated vertex [v.sub.n+1] to [G.sub.2] to get a realization of F'.
Further suppose that [[upsilon].sub.i] is a free vertex of (G, m), and G' is the induced sub-graph on the vertex set [V.sub.G] {[[upsilon].sub.i]}, along with the isolated vertex [[upsilon].sub.i].
If x is an isolated vertex, the (OSCL) is obviously satisfied.
If b is incident with each of [F.sub.0], then X[Q.sup.k.sub.n] - F has two components, one of which is an isolated vertex. If b is not incident with each of [F.sub.0], then X[Q.sup.k.sub.n] - F is connected; a contradiction to that F is an edge cut of X[Q.sup.k.sub.n].
Due to the existence of the isolated vertex, there is always at least one path of infinity length in the password graph, even if we remove the vertices with 0 degrees and calculate again; the same reason for connectivity: due to the existence of isolated clusters, the diameter for filtered password graph is still +[infinity], and the result is also listed in Table 2.
Also, if G has an isolated vertex, [M.sub.k] (G) does not exists.
2.6 Definition  A vertex which is not incident with any edge is called an isolated vertex. In other words a vertex with degree zero is called an isolated vertex.
Let {[v.sub.1], [v.sub.2], [v.sub.3]} be the path in < S > and [v.sub.4] be a isolated vertex in < S > .
A vertex [v.sub.j] [member of] V of interval valued neutrosophic graph G = (A, B) is said to be an isolated vertex if there is no effective edge incident at [v.sub.j].
Let [C.sub.6] be a cycle of length six and [GAMMA] be a graph obtained by connecting an isolated vertex to one of the vertices of [C.sub.6].
Vertex of degree zero is called an isolated vertex. Vertex of degree one is called a pendant.
If there exist one or more groups of connected vertices from [N.sub.i0], and there is an edge between i and some isolated vertex from [N.sub.i0], we delete the edge between i and the vertex and add an edge between i and a vertex chosen from the largestgroup randomly.

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