https://file.aiquickdraw.com/mathbot/file/1725495680137lfj1t4vg.jpg

To determine which graph is connected, we need to understand the definition of a connected graph. A graph is considered *connected* if there is a path between any pair of vertices in the graph.

Let's analyze each graph in the image:

- **Graph A**: The vertices are A, B, C, and D. You can see that all vertices are connected directly or indirectly by edges, which means there's a path from any vertex to any other vertex.
- **Graph B**: The vertices are A, B, C, D, and E. Vertex E is only connected to vertex B, and there is no path to vertices C or D. Therefore, this graph is *not connected*.
- **Graph C**: The vertices are A, B, C, D, and E. All vertices are connected directly or indirectly by edges, so there's a path from any vertex to any other vertex.

**Conclusion**:
- **Graph A** is connected.
- **Graph B** is not connected.
- **Graph C** is connected.

Therefore, the correct answer is **both A and C** are connected. However, based on the provided answer options in the image, if the intention was to select one graph, **Graph C** would be the correct choice because it's the only one with all vertices and edges clearly connected.

Would you like more details, or do you have any questions? Here are some related questions:

1. What is the difference between a connected graph and a complete graph?
2. How do you determine if a graph is disconnected?
3. What are the properties of a graph that can influence its connectivity?
4. Can a graph be connected if it contains isolated vertices?
5. How do bridges (or cut-edges) in a graph affect its connectivity?

**Tip:** When analyzing graphs, always check if there's a path between all pairs of vertices to confirm connectivity.

Which graph is connected? (Options A, B, C are provided with different graph structures)

Analyze different graphs to determine which one is connected. This problem involves understanding the definition of a connected graph, a key concept in graph theory. Suitable for high school students in Grades 9-12.

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