Definition:Component of Graph
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Definition
Let $G$ be a graph.
Let $H$ be a subgraph of $G$ such that:
- $H$ is connected
- $H$ is not contained in any connected subgraph of $G$ which has more vertices or edges than $H$ has.
Then $H$ is a component of $G$.
Example
This graph has $4$ components:
Also see
- Definition:Connected Graph: a graph with only one component.
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 2.3$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): component (of a graph)