Formulas for the Number of Spanning Trees in a Fan
Zbigniew R. Bogdanowicz · 2008
Let Pn be a simple path on n vertices. An n-fan is a simple graph G formed from a path Pn by adding a vertex adjacent to every vertex of Pn. In this work we denote n-fan by Fn+1 and derive the explicit formula for t(Fn+1) the number of spanning trees in Fn+1 to be t(Fn+1 )=2 ((3− √ 5)/2) n+1 −((3+ √ 5)/2) n�1 5−3 √ 5 . In addition, we show that