https://file.aiquickdraw.com/mathbot/file/1729474300742k69i3e55.jpg

The graph in the image shows several vertices labeled \( V_1, V_2, \ldots, V_8 \), with various edges connecting these vertices. The question asks which vertices are adjacent to vertex \( V_6 \).

Looking at the graph:
- **Adjacent vertices** are those that are directly connected by an edge.
- Vertex \( V_6 \) has edges connecting it to the following vertices:
  1. \( V_2 \)
  2. \( V_3 \)
  3. \( V_4 \)
  4. \( V_7 \)

Thus, the vertices adjacent to \( V_6 \) are:
- \( V_2 \)
- \( V_3 \)
- \( V_4 \)
- \( V_7 \)

So, the correct options from the list are:
- B. \( V_2 \)
- D. \( V_3 \)
- E. \( V_4 \)
- G. \( V_7 \)

Would you like more details on graph theory, or do you have any questions?

### Related Questions:
1. What is the definition of an adjacent vertex in a graph?
2. How do we distinguish between directed and undirected graphs?
3. What is a loop in graph theory, and does \( V_6 \) have one in this graph?
4. Can there be graphs where a vertex has no adjacent vertices?
5. What are the degrees of vertices in a graph, and how can we calculate them for this graph?

### Tip:
In graph theory, the **degree** of a vertex refers to the number of edges connected to it. For undirected graphs, loops count as two.

Which of the following vertices are adjacent to vertex V_6?

Learn how to identify adjacent vertices in a graph. In this problem, we examine which vertices are adjacent to vertex V_6 based on the graph's edges. Suitable for students in Grades 9-12 studying graph theory.

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