# trivial graph

## trivial graph

[′triv·ē·əl ¦graf]
(mathematics)
A graph with one vertex and no edges.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Notice that every non trivial graph G contains at least one k-monopoly, with k [member of] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], since every vertex of G satisfies the k-monopoly condition for the whole vertex set V(G).
(a) The trivial graph K1 is the only graph with distance pattern distinguishing number as the order of that graph.
First, it is clear that for a trivial graph one can check in linear time whether it admits a cct.
For a vertex v of a graph G, the lower connectivity, denoted by [s.sub.v](G), is the smallest number of vertices that contains v and those vertices whose deletion from G produces a disconnected or a trivial graph. We observe that
The best known and most useful measures of how well a graph is connected is the connectivity, defined to be the minimum number of vertices in a set whose deletion results in a disconnected or trivial graph. As the connectivity is the worst-case measure, it does not always reflect what happens throughout the graph.
Let u be a center of G and let [H.sub.0] be the trivial graph with vertex set {u}.
The connectivity [kappa] (G) of a connected graph G is the minimum number of vertices whose removal results in a disconnected or trivial graph.
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