Question: For a graph to have an Eulerian circuit ( a circuit that traverses every edge exactly once and ends at the starting vertex ) ,

For a graph to have an Eulerian circuit (a circuit that traverses every edge exactly once and ends at the starting vertex), every vertex must have an even degree.
In your description, you provided the degrees of each vertex:
A: 4 degrees
B: 2 degrees
C: 4 degrees
D: 3 degrees
E: 2 degrees
F: 1 degree

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