|Example 1: Finding an Euler circuit
All of the vertices have even degree except B (degree 3) and D (degree 3). According to Euler's Theorems, there is no Euler circuit for this graph. (However, there is an Euler path, starting at one of the odd vertices and ending at the other).
Example 1: Finding a Hamilton circuit
One possible solution: AGFECDBA
Example 2: Finding an Euler circuit
Since there are no odd vertices, there is an Euler circuit.
One possible solution: AGFADCFECBA
Example 2: Finding a Hamilton circuit
There is no Hamilton circuit.