To determine which of the graphs are trees, let's review the characteristics of a tree:

1. A tree is a connected graph with no cycles.
2. A tree with $n$ vertices has exactly $n - 1$ edges.

Let's examine each graph:

• Graph A: There are cycles present, as each vertex is connected in such a way that multiple paths can form loops. Therefore, it is not a tree.

• Graph B: This graph is connected, but there are cycles evident in its structure as well. So, it is not a tree.

• Graph C: There are also cycles here, indicating it is not a tree.

• Graph D: This graph has no cycles and is connected. Additionally, the number of edges is exactly one less than the number of vertices, meeting the criteria for a tree. Graph D is a tree.

Conclusion: The correct answer is Graph D.

Would you like further details or have any questions about this?

Here are some additional questions to deepen your understanding:

1. What is the difference between a tree and a forest in graph theory?
2. How can we identify cycles in a graph efficiently?
3. What are the applications of trees in computer science?
4. How does the concept of a Minimum Spanning Tree relate to this problem?
5. What are the properties of binary trees compared to general trees?

Tip: A quick way to check if a graph is a tree is to confirm it's connected and verify it has $n - 1$ edges for $n$ vertices, which eliminates the need for cycle detection.