1 The graph \(\mathrm { K } _ { 5 }\) has five nodes, \(A , B , C , D\) and \(E\), and there is an arc joining every node to every other node.
- Draw the graph \(\mathrm { K } _ { 5 }\) and state how you know that it is Eulerian.
- By listing the arcs involved, give an example of a path in \(\mathrm { K } _ { 5 }\). (Your path must include more than one arc.)
- By listing the arcs involved, give an example of a cycle in \(\mathrm { K } _ { 5 }\).