https://file.aiquickdraw.com/mathbot/file/1728702894885eqeiurf0.jpg

Tentukan diketahui sebuah graf berarah E dengan himpunan V={v1, v2, v3, v4, v5} dan himpunan arah E={(v1, v2) (v2, v3) (v3, v4) (v4, v1) (v5, v5) (v5, v1)}gambar lah diagram dari graf E

The problem asks you to draw a directed graph (or *digraph*) \( E \) based on the given sets:

1. **Vertices (V):**  
   \( V = \{v_1, v_2, v_3, v_4, v_5\} \)

2. **Edges (E):**  
   \( E = \{(v_1, v_2), (v_2, v_3), (v_3, v_4), (v_4, v_1), (v_5, v_5), (v_5, v_1)\} \)

### Steps to draw the directed graph:
1. **Vertices:** Place 5 vertices labeled \( v_1, v_2, v_3, v_4, v_5 \).
2. **Edges:** Connect the vertices with directed edges (arrows) based on the following pairs:
   - \( (v_1, v_2) \): Draw an arrow from \( v_1 \) to \( v_2 \).
   - \( (v_2, v_3) \): Draw an arrow from \( v_2 \) to \( v_3 \).
   - \( (v_3, v_4) \): Draw an arrow from \( v_3 \) to \( v_4 \).
   - \( (v_4, v_1) \): Draw an arrow from \( v_4 \) to \( v_1 \), forming a cycle with \( v_1, v_2, v_3, v_4 \).
   - \( (v_5, v_5) \): Draw a loop from \( v_5 \) to itself.
   - \( (v_5, v_1) \): Draw an arrow from \( v_5 \) to \( v_1 \).

This will result in a directed graph where:
- There is a cycle connecting \( v_1, v_2, v_3, v_4 \),
- \( v_5 \) has a self-loop and is connected to \( v_1 \).

Would you like a detailed image of the graph or further clarification?

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Here are 5 related questions to expand your understanding:
1. What is the difference between directed and undirected graphs?
2. How do you identify cycles in directed graphs?
3. What are the in-degrees and out-degrees of each vertex in this graph?
4. What are the practical applications of directed graphs?
5. How do self-loops affect the structure of a graph?

**Tip:** In a directed graph, the direction of edges is crucial for understanding relationships between vertices, unlike in an undirected graph.

Tentukan diketahui sebuah graf berarah E dengan himpunan V = {v1, v2, v3, v4, v5} dan himpunan arah E = {(v1, v2), (v2, v3), (v3, v4), (v4, v1), (v5, v5), (v5, v1)} gambarlah diagram dari graf E

Learn how to draw a directed graph for the vertex set V = {v1, v2, v3, v4, v5} and edge set E = {(v1, v2), (v2, v3), (v3, v4), (v4, v1), (v5, v5), (v5, v1)}. This problem covers concepts in graph theory, including directed edges, graph cycles, and self-loops. Suitable for university-level students.

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