Let A={a
1
,…,a
n
} be a set with n≥3 elements and let c∈
/
A. Construct a graph G=(V,E) as follows. The set of vertices is V=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 specifed above. (a) [5 pts] Express the number of paths of length 2 in G in terms of n. Justify your answer. (b) [5 pts] Express the number of cycles in G in terms of n. Justify your answer.
