To determine if this graph is a tree, let's review what a tree graph requires:

1. Connectedness: A tree must be connected, meaning there should be a path between any two vertices.
2. No Circuits: A tree must not contain any cycles (closed loops or circuits).

Analyzing the Graph:

The given graph has several loops (cycles), specifically squares, which indicate the presence of circuits. Additionally, the graph is fully connected since each vertex is reachable from others. However, due to the presence of circuits, it does not satisfy the requirements of a tree.

Conclusion:

The correct answer is:

• The graph is not a tree because it has a circuit.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. What are the key characteristics that define a tree in graph theory?
2. How can one identify cycles in a graph?
3. Why is connectedness essential for a tree, and how is it checked?
4. Can a tree have more edges than vertices?
5. How does a minimum spanning tree differ from a regular tree?

Tip: In a tree, the number of edges is always one less than the number of vertices (for an undirected graph with no cycles).