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Math Help - component

  1. #1
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    component

    How do you prove that a graph is connected iff it has exactly one component?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    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.
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  3. #3
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    Quote Originally Posted by Plato View Post
    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?
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  4. #4
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    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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