Every tree must have at least two vertices of degree one.
A) This statement is always true.
B) This statement is always false.
C) This statement is only true if there are more than four vertices.
D) This statement is only false if there are more than four vertices.
E) None of the above.

Question

Every tree must have at least two vertices of degree one. 
A) This statement is always true.
B) This statement is always false.
C) This statement is only true if there are more than four vertices.
D) This statement is only false if there are more than four vertices.
E) None of the above.

Quizplus · Accepted Answer

In a tree, which is a connected acyclic graph, there must be at least two leaves (vertices of degree one) because removing a leaf from a tree reduces the number of vertices by one and the number of edges by one, maintaining the tree structure.

Every Tree Must Have at Least Two Vertices of Degree