3 Consider the following algorithm.
Step 1: Input a positive integer \(n\).
Step 2 : Draw a graph consisting of \(n\) vertices and no arcs.
Step 3 : Create a new vertex and join it directly to every vertex of order 0.
Step 4: Create a new vertex and join it directly to every vertex of odd order.
Step 5 : Stop.

1. Draw separate diagrams to show the result of applying this algorithm in the following cases.
   (a) \(n = 1\)
   (b) \(n = 2\)
   (c) \(n = 3\)
   (d) \(n = 4\)
2. State how many arcs are in the graph that results when the algorithm is applied to a set of \(n\) vertices.