Question

a graph has ten vertices and thirteen edges. the graph has no loops or multiple edges. which one of the statements below applies to this description?
the described graph is a tree.
the described graph is not a tree.
the described graph may or may not be a tree.

Explanation:

Step1: Recall the tree property

A tree with \( n \) vertices has exactly \( n - 1 \) edges. Here, \( n = 10 \), so a tree should have \( 10 - 1 = 9 \) edges.

Step2: Compare with given edges

The graph has 13 edges, which is more than 9. Also, a tree is acyclic and connected, and has \( n - 1 \) edges. Since the number of edges here (\( 13 \)) is not \( n - 1 \) (\( 9 \)), the graph is not a tree.

Answer:

The described graph is not a tree.