https://file.aiquickdraw.com/mathbot/file/1727248954943lxy02tog.jpg

To represent the given graphs using an adjacency list, we will list the neighbors for each vertex based on the directed edges shown in each graph. Here are the adjacency lists for the graphs numbered 1-4.

### Graph 1:
Vertices: \(a, b, c, d\)
- \(a \rightarrow b, d\)
- \(b \rightarrow a, c\)
- \(c \rightarrow b, d\)
- \(d \rightarrow a, c\)

**Adjacency List:**
- \(a: b, d\)
- \(b: a, c\)
- \(c: b, d\)
- \(d: a, c\)

### Graph 2:
Vertices: \(a, b, c, d, e\)
- \(a \rightarrow b, d\)
- \(b \rightarrow a, c, d\)
- \(c \rightarrow e\)
- \(d \rightarrow c, e\)
- \(e\) (no outgoing edges)

**Adjacency List:**
- \(a: b, d\)
- \(b: a, c, d\)
- \(c: e\)
- \(d: c, e\)
- \(e:\) (no outgoing edges)

### Graph 3:
Vertices: \(a, b, c, d\)
- \(a \rightarrow b, d\)
- \(b \rightarrow a, c, d\)
- \(c \rightarrow a, d\)
- \(d \rightarrow a, b, c\)

**Adjacency List:**
- \(a: b, d\)
- \(b: a, c, d\)
- \(c: a, d\)
- \(d: a, b, c\)

### Graph 4:
Vertices: \(a, b, c, d, e\)
- \(a \rightarrow b, c, d\)
- \(b \rightarrow a, d, e\)
- \(c \rightarrow a, b, e\)
- \(d \rightarrow b, c, e\)
- \(e \rightarrow a, d\)

**Adjacency List:**
- \(a: b, c, d\)
- \(b: a, d, e\)
- \(c: a, b, e\)
- \(d: b, c, e\)
- \(e: a, d\)

Would you like a more detailed explanation of adjacency lists, or do you have any questions?

### Related questions:
1. How is an adjacency list different from an adjacency matrix?
2. What is the time complexity of searching for edges in an adjacency list?
3. How would you represent a weighted graph using an adjacency list?
4. Can an adjacency list be used for undirected graphs?
5. How would you implement depth-first search (DFS) on a graph represented by an adjacency list?

**Tip:** Adjacency lists are more space-efficient for sparse graphs compared to adjacency matrices.

Use an adjacency list to represent the given graphs.

Learn how to represent four directed graphs using an adjacency list. Each graph's vertices and directed edges are analyzed to generate the appropriate adjacency list. Suitable for high school students learning graph theory.

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