To identify a cycle containing vertex $A$ in this graph, we look for a path that begins and ends at $A$ while passing through at least two other distinct vertices.

One possible cycle containing $A$ is: $A - B - C - D - A$

This cycle goes from $A$ to $B$, then $B$ to $C$, $C$ to $D$, and finally returns to $A$.

If you have any further questions or need additional cycles, feel free to ask!

Related Questions

1. Can you list a different cycle that includes vertex $A$?
2. How many distinct cycles are there in this graph?
3. What is the degree of vertex $A$ in this graph?
4. Can you identify a cycle that contains vertex $E$?
5. Is this graph connected, meaning there is a path between any two vertices?

Tip: When looking for cycles in a graph, start at a vertex and trace paths that return to the starting point without revisiting edges.