Let A={a₁, a₂,...a_n} be a set with n 3 elements and let cA. Construct a graph G = ( V, E ) as follows. The set of vertices isV=A{c} and the set of edges E is defined by

• The subgraph of G induced by A is a cycle.
• There is an edge between c and every vertex in A.
• There are no other edges except those specified above.

1. Express the number of paths of length 2 in G in terms of n.
2. Express the number of cycles in G in terms of n.