4. (a) Explain why it is not possible to draw a graph with exactly 5 nodes with orders \(1,3,4,4\) and 5 A connected graph has exactly 5 nodes and contains 18 arcs. The orders of the 5 nodes are \(2 ^ { 2 x } - 1,2 ^ { x } , x + 1,2 ^ { x + 1 } - 3\) and \(11 - x\).
(b) (i) Calculate X .
(ii) State whether the graph is Eulerian, semi-Eulerian or neither. You must justify your answer.
(c) Draw a graph which satisfies all of the following conditions:

• The graph has exactly 5 nodes.
• The nodes have orders 2, 2, 4, 4 and 4
• The graph is not Eulerian.