#### Answer

The path A,E,D,C,B,A is a Hamilton circuit that begins as A,E...

#### Work Step by Step

A Hamilton path is a sequence of adjacent vertices that visits each vertex in the graph exactly once. A Hamilton circuit is a Hamilton path that begins and ends at the same vertex.
Let's start at vertex A. The path can travel to vertex E, and then to vertex D. After this step, the path must travel to vertex C, then to vertex B, and then finally back to vertex A.
This path is A,E,D,C,B,A. Since this path visits every vertex in the graph exactly once, this path is a Hamilton path. Since this Hamilton path starts and ends at the same vertex, this path is a Hamilton circuit.
This is one Hamilton circuit that begins as A,E,..., but there are other such Hamilton circuits in the graph.