For n ¥ 1, let tn count the number of spanning trees for the fan on n + 1 vertices.
(a) Show that tn+1 = tn + nl=0 tl, where n ¥ 1 and t0 = 1.
(b) For n ¥ 2, show that tn+1 = 3tn - tn-1.
(c) Solve the recurrence relation in part (b) and show that for n ¥ 1, tn = F2n, the 2nth Fibonacci number.
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Question Posted: June 21, 2016 08:56:27