Exercise · ZW-CONNECTED-GRAPH-002 · ★☆☆ Basic
A graph with vertices \(1,\dots,5\) has edges \(12\), \(23\) and \(45\). How many connected components does it have?
Choose one option.
Show answer
- B. 2
Explanation
The components are \(\{1,2,3\}\) and \(\{4,5\}\): no path joins a vertex of the first group to one of the second.
Review the concept: Connected graph
A graph \(G=(V,E)\) is connected if any two vertices \(u,v\in V\) are joined by a path.
\[\forall\,u,v\in V\ \ \exists\ \text{path from } u \text{ to } v\]
More practice problems: connected graph
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