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A fan of order $n$ is a graph on the vertices $\{0, 1, \dots, n\}$ with 2n − 1 edges defined as follows: vertex 0 is connected by an edge to each of the other $n$ vertices, and vertex $i$ is connected by an edge to vertex $i + 1$, for $1 \leq i \leq n − 1$.

Let $f_n$ denote the number of spanning trees of the fan of order $n$.

  1. Calculate $f_4$.
  2. Write a recurrence for $f_n$.
  3. Solve for fn using ordinary generating fuctions.
asked in Graph Theory by Veteran (79.1k points)   | 108 views

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