Questions: Determine whether the graph is a tree. If not, explain why it is not Choose the correct answer. A. The graph is a tree. B. The graph is not a tree because it has one or more circuits. C. The graph is not a tree because it is disconnected.

Determine whether the graph is a tree. If not, explain why it is not

Choose the correct answer.
A. The graph is a tree.
B. The graph is not a tree because it has one or more circuits.
C. The graph is not a tree because it is disconnected.

Transcript text: Determine whether the graph is a tree. If not, explain why it is not Choose the correct answer. A. The graph is a tree. B. The graph is not a tree because it has one or more circuits. C. The graph is not a tree because it is disconnected.

Solution

Solution Steps

Step 1: Identify the properties of a tree

A tree is a connected graph with no cycles. This means that there is a path between any two vertices, and there are no closed loops.

Step 2: Check for connectivity

Examine the graph to see if all vertices are connected. In the given graph, there are two separate components: one containing vertices A, G, I, J, and H, and another containing vertices B, D, E, C, and F. Since the graph is not connected, it fails the connectivity requirement of a tree.

Step 3: Check for cycles

Even though the graph is already determined to be disconnected, we can also check for cycles. In both components, there are no cycles present. However, this check is redundant since the graph is already disqualified as a tree due to being disconnected.

Final Answer

The graph is not a tree because it is disconnected. (Option C)

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