Let's analyze the graph in the image and answer the questions step by step.

1. Is the graph depicted in the image a tree?
   A tree is a connected graph with no cycles. It appears that the graph in the image is connected and has no cycles, as it is branching out. Therefore, this graph is a tree.

2. How many edges does the graph have?
   In the graph, edges are the connections between the vertices. From the image, we count the total number of edges.
   The graph has 7 edges.

3. How many vertices are in the graph?
   Vertices are the points where the edges meet. The graph has a total of 8 vertices.

4. How many terminal vertices does the graph have?
   Terminal vertices (or leaves) are vertices with only one connecting edge. From the graph, we observe 4 terminal vertices.

Would you like to dive into more details on any of these aspects? Let me know if you have any questions.

Here are some related questions:

1. What is the difference between a tree and a general graph?
2. How can we check if a graph is a tree using properties like connectivity and cycles?
3. How do we calculate the number of edges in a tree based on the number of vertices?
4. What are the properties of terminal vertices in trees?
5. How does a graph with cycles differ from a tree?

Tip: In any tree graph, the number of edges is always one less than the number of vertices.