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Fully connected graphs

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Is it TRUE or FALSE that ( and why )

In an undirected graph(with no self loops), if every vertex has degree at least n/2, then the graph is fully connected ?

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https://brainmass.com/computer-science/computer-systems-organization/fully-connected-graphs-45266

Solution Preview

True.

For a fully connected graph, every vertex has an edge to every other vertex.
DIRAC'S Theorem: if G is a simple graph with n vertices with n ≥ 3 ...

Solution Summary

Fully connected graph overview

$2.19