Analyze the prove that a tree with n vertices has n-1 edges.
Examples
Input:"test_input_1"
Output:"output_1"
Input:"test_input_2"
Output:"output_2"
Hints
Recall that a tree is a connected acyclic graph. How does this definition relate to the number of edges in the graph?
Consider using mathematical induction on the number of vertices to prove the statement. What would be the base case and the inductive step?
Prove the statement by contradiction. Assume there exists a tree with n vertices and more than n-1 edges, then derive a contradiction using properties of trees and connected graphs.
Prove that a tree with n vertices has n-1 edges
Analyze the prove that a tree with n vertices has n-1 edges.