Question:
How many edges will a tree with $ n $ vertices have?
How many edges will a tree with $ n $ vertices have?
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Remember that in any tree, the number of edges is always one less than the number of vertices.
Updated On: May 3, 2025
- \( \left\lfloor \frac{n}{2} \right\rfloor \)
- \( n \)
- \( 2 \times n \)
- \( n - 1 \)
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The Correct Option is D
Solution and Explanation
A tree is a connected acyclic graph. It is a fundamental property of trees that a tree with \( n \) vertices always has \( n - 1 \) edges. This is because, in a tree, there are no cycles, and adding any extra edge would create a cycle.
Thus, the number of edges in a tree with \( n \) vertices is \( n - 1 \).
Thus, the number of edges in a tree with \( n \) vertices is \( n - 1 \).
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