To find a Hamiltonian circuit in the given graph, we need to create a path that visits each vertex exactly once and returns to the starting point.

Steps

1. Identify all vertices: A, B, C, D, and E.
2. Observe that each vertex is connected to others, forming a complete graph with multiple paths possible.

One possible Hamiltonian circuit, starting and ending at vertex A, could be:

A → B → C → D → E → A

Verification

This path:

• Visits each vertex once.
• Returns to the starting vertex (A).

Let me know if you'd like more details or have questions!

Here are some related questions to consider:

1. What is a Hamiltonian circuit, and how is it different from an Eulerian circuit?
2. Are there other possible Hamiltonian circuits for this graph?
3. How can we determine if a graph has a Hamiltonian circuit in general?
4. What is the difference between a Hamiltonian path and a Hamiltonian circuit?
5. How does the concept of graph completeness affect the existence of Hamiltonian circuits?

Tip: In a complete graph, every vertex is connected to every other vertex, which often makes finding Hamiltonian circuits easier.