# Definition:Connected (Graph Theory)/Graph

< Definition:Connected (Graph Theory)(Redirected from Definition:Connected Graph)

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## Contents

## Definition

Let $G$ be a graph.

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

### Disconnected

Let $G$ be a graph.

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

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

## Also see

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 2.3$: Connected Graphs