How do you prove that a graph is connected iff it has exactly one component?
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Originally Posted by alexandrabel90 How do you prove that a graph is connected iff it has exactly one component? Good grief, a component of a graph is a maximally connectively subgraph.
Originally Posted by Plato Good grief, a component of a graph is a maximally connectively subgraph. But how do i prove that a cOnnected graph has only one component? Cant it have two?
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.
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