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The problem asks to find the edges in the minimum spanning tree (MST) of the given graph. To solve this, I will apply **Kruskal's algorithm** or **Prim's algorithm** to identify the MST.

**Steps for Kruskal’s Algorithm:**
1. Sort all edges by increasing weight.
2. Start adding the edges to the MST, ensuring no cycles are formed.
3. Continue until all vertices are connected.

### The edges, sorted by weight:
1. \( (i, h) = 1 \)
2. \( (d, f) = 1 \)
3. \( (h, f) = 3 \)
4. \( (e, f) = 4 \)
5. \( (a, e) = 5 \)
6. \( (b, e) = 6 \)
7. \( (d, g) = 7 \)
8. \( (c, g) = 8 \)
9. \( (g, h) = 10 \)
10. \( (e, g) = 11 \)
11. \( (a, b) = 12 \)
12. \( (f, c) = 13 \)

Now, starting with the smallest edge and adding it step by step:

1. Add \( (i, h) \) with weight 1.
2. Add \( (d, f) \) with weight 1.
3. Add \( (h, f) \) with weight 3.
4. Add \( (e, f) \) with weight 4.
5. Add \( (a, e) \) with weight 5.
6. Add \( (b, e) \) with weight 6.
7. Add \( (d, g) \) with weight 7.

At this point, all vertices are connected and the tree is complete. The total weight is minimized.

### Edges in the MST:
- \( (i, h) \)
- \( (d, f) \)
- \( (h, f) \)
- \( (e, f) \)
- \( (a, e) \)
- \( (b, e) \)
- \( (d, g) \)

### The correct answer is **Option B**.

Would you like a detailed explanation of any of these steps?

Here are some related questions you might find useful:
1. What is Prim's algorithm, and how does it compare to Kruskal's?
2. How do you check if adding an edge forms a cycle in a graph?
3. What are other real-world applications of Minimum Spanning Trees?
4. How do you implement Kruskal’s algorithm programmatically?
5. What is the time complexity of Kruskal's and Prim's algorithms?

**Tip:** When solving graph problems, always visualize the connections between vertices and ensure no cycles are formed when constructing a tree.

What are the edges in the minimum spanning tree of the graph shown?

Learn how to find the edges of a minimum spanning tree using Kruskal's algorithm. This problem covers key concepts in graph theory, including sorting edges by weight and ensuring no cycles are formed. Suitable for students in Grades 10-12.

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