# Math Help - component

1. ## component

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

2. 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.

3. 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?

4. 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.