Questions: Determine whether or not the graph is a tree. If it is not, explain why. This graph is a tree. This graph is not a tree. The graph has one or more circuits. Every edge is a bridge.

Determine whether or not the graph is a tree. If it is not, explain why. This graph is a tree. This graph is not a tree. The graph has one or more circuits. Every edge is a bridge.
Transcript text: Determine whether or not the graph is a tree. If it is not, explain why. This graph is a tree. This graph is not a tree. The graph has one or more circuits. Every edge is a bridge.
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Solution

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Solution Steps

Step 1: Determine if the graph is a tree

A tree is a connected graph with no cycles and \( n \) vertices and \( n-1 \) edges.

Step 2: Check for cycles

Examine the graph for any cycles. A cycle is a path that starts and ends at the same vertex without repeating any edges or vertices.

Step 3: Count vertices and edges

Count the number of vertices and edges in the graph. For a graph to be a tree, it must have \( n-1 \) edges if it has \( n \) vertices.

Final Answer

The graph is not a tree because it contains a cycle (A-B-D-A).

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