Which of the following scenarios results in a graph which is a tree?
A) A connected graph with 5 vertices and 4 edges.
B) A graph in which every edge is a bridge.
C) A graph in which every pair of vertices has one unique path which connects them.
D) All of the above.
E) None of the above.

Question

Which of the following scenarios results in a graph which is a tree? 
A) A connected graph with 5 vertices and 4 edges.
B) A graph in which every edge is a bridge.
C) A graph in which every pair of vertices has one unique path which connects them.
D) All of the above.
E) None of the above.

Quizplus · Accepted Answer

All the given scenarios describe properties of a tree. A) A connected graph with $n$ vertices and $n-1$ edges is a tree. B) In a tree, every edge is a bridge (removing it increases the number of connected components). C) A tree ensures exactly one unique path between any two vertices.

Which of the Following Scenarios Results in a Graph Which