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Fully connected graphs

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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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 ...

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Fully connected graph overview