How do you prove that a graph is connected iff it has exactly one component?

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- Feb 17th 2011, 04:46 PMalexandrabel90component
How do you prove that a graph is connected iff it has exactly one component?

- Feb 17th 2011, 05:17 PMPlato
- Feb 17th 2011, 05:19 PMalexandrabel90
- Feb 18th 2011, 12:24 AMemakarov
By definition, a component is not connected to vertices outside of it. In a connected graph, any proper subgraph (not equal to the original graph) is connected to some outside vertex; therefore, such subgraph is not a component.