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The problem involves finding the shortest path from vertex A to vertex B in a weighted graph. Each edge in the graph has a weight associated with it, representing the distance between two vertices. I will use Dijkstra's algorithm to find the shortest path from vertex A to vertex B.

### Steps:
1. Identify all vertices: \(A\), \(B\), \(C\), \(D\), and \(E\).
2. List the edges and their weights:
   - \( A \to B: 9 \)
   - \( A \to C: 6 \)
   - \( A \to D: 20 \)
   - \( A \to E: 17 \)
   - \( B \to C: 7 \)
   - \( B \to E: 27 \)
   - \( C \to D: 24 \)
   - \( D \to E: 30 \)

Next, I will calculate the shortest path using Dijkstra's algorithm.

Let me compute this path for you.The shortest path from vertex \( A \) to vertex \( B \) is through the direct edge between them, with a total distance of **9**. The path is simply \( A \to B \).

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:
1. How does Dijkstra's algorithm work in weighted graphs?
2. Can Dijkstra’s algorithm handle negative weights?
3. What is the time complexity of Dijkstra's algorithm for a graph with \( n \) vertices?
4. How would the shortest path change if the weights on edges were dynamic?
5. How does Dijkstra’s algorithm differ from the Bellman-Ford algorithm?

**Tip**: Dijkstra's algorithm is efficient when all edge weights are positive, but for graphs with negative weights, consider using Bellman-Ford's algorithm instead.

Find the length of the shortest path from vertex A to vertex B.

Learn how to find the shortest path between vertex A and vertex B in a weighted graph using Dijkstra's Algorithm. This problem demonstrates key concepts in graph theory and is suitable for high school students.

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