Spanning forests and the golden ratio

For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path, the fij's can be expressed as the products of Fibonacci numbers; for a cycle, they are products of Fibonacci and Lucas numbers. The doubly stochastic graph matrix is the matrix F = (fij )n

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Pavel Chebotarev
• Keywords: DAM 2008, Graph Vertices, Matrix Forest Theorem, Stochastic Graph Matrix