Definition:Connected (Graph Theory)/Graph

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Let $G$ be a graph.

Then $G$ is connected if and only if every pair of vertices in $G$ is connected.


Let $G = \struct {V, E}$ be a graph.

Then $G$ is disconnected if and only if it is not connected.

That is, if and only if there exists (at least) two vertices $u, v \in V$ such that $u$ and $v$ are not connected.

Also see

  • Results about connected graphs can be found here.