Question:
For a given graph G having \( v \) vertices and \( e \) edges which is connected and has no cycles, which of the following statements is true?
For a given graph G having \( v \) vertices and \( e \) edges which is connected and has no cycles, which of the following statements is true?
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For any tree, the relationship between the number of vertices and edges is \( e = v - 1 \). This property is useful for solving problems involving trees.
Updated On: Jun 16, 2025
- \( v = e \)
- \( v = e + 1 \)
- \( v + 1 = e \)
- \( v = e - 1 \)
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The Correct Option is B
Solution and Explanation
In a connected graph with no cycles, we have a tree. For a tree, it is known that the number of edges \( e \) is always one less than the number of vertices \( v \). This relationship is given by the equation:
\[
e = v - 1
\]
Rearranging, we get:
\[
v = e + 1
\]
Thus, the correct answer is option (2).
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