Definition:Connected (Graph Theory)/Graph
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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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: walk
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: walk
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: connected graph