Question: Let A={a 1 , a 2 ,...a n } be a set with n 3 elements and let c A . Construct a graph G

Let A={a1, a2,...an} 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.

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