In any tree with n vertices, how many edges does the tree have?

• A. n-1
• B. n
• C. n+1
• D. 2n

Answer: (A)

In a tree, you have to connect all n vertices without forming any cycles. To connect n vertices in a connected acyclic way, you need exactly n−1 edges. You can see this by building the tree step by step: start with one vertex (0 edges), then add each new vertex and connect it with one edge to the existing tree. Each addition increases both the vertex count by 1 and the edge count by 1, so after reaching n vertices you’ve added n−1 edges. This can also be framed as an induction: a single-vertex tree has 0 edges, and adding one vertex with one connecting edge preserves the n−1 edge count for all n. If you had n edges, you’d must introduce a cycle, which isn’t allowed in a tree. Therefore, the number of edges is n−1.