5. (20 points) Give examples of the following graphs or explain why such examples cannot exist only simple graphs allowed, i.e., there can be only one edge between two vertices). Recll that a Hamilton cycle (also called Rudrata cycle) visits each vertex only once (except for the each type of cycle (as per the question). (a) A graph with a Hamilton cycle but with no Eulerian cycle (b) A graph with an Eulerian cycle but with no Hamilton cycle (c) A graph with both a Hamilton and Eulerian cycle. (d graph with a cycle that includes all vertices, but with neither a Hamilton nor an Eulerian cycle. ) A