3 A simple graph is one in which any two vertices are directly connected by at most one arc and no vertex is directly connected to itself. A connected graph is one in which every vertex is connected, directly or indirectly, to every other vertex. A simply connected graph is one that is both simple and connected.

1. A simply connected graph is drawn with 6 vertices and 9 arcs.
   (a) What is the sum of the orders of the vertices?
   (b) Explain why if the graph has two vertices of order 5 it cannot have any vertices of order 1.
   (c) Explain why the graph cannot have three vertices of order 5 .
2. Draw an example of a simply connected graph with 6 vertices and 9 arcs in which one of the vertices has order 5 and all the orders of the vertices are odd numbers.
3. Draw an example of a simply connected graph with 6 vertices and 9 arcs that is also Eulerian.