[Graphs generated by this script: initPicture(0,300,0,250);dot([50,187.5],"closed");text([50,187.5],'A',above);dot([150,187.5],"closed");text([150,187.5],'B',above);dot([150,62.5],"closed");text([150,62.5],'C',below);dot([250,187.5],"closed");text([250,187.5],'D',above);dot([250,62.5],"closed");text([250,62.5],'E',below);line([50,187.5],[150,62.5]);line([50,187.5],[250,62.5]);line([150,187.5],[150,62.5]);line([150,62.5],[250,187.5]);line([150,62.5],[250,62.5]);line([250,187.5],[250,62.5]);]

Is a Hamilton circuit possible for this graph? If so, give your answer as a list of vertices, starting and ending at the same vertex. Example: ABCA If it is not possible, enter DNE.



Is a Hamilton path possible for the given graph? If so, give your answer as a list of vertices, for example, ABCD. If it is not possible, enter DNE.