The number of spanning trees in regular graphs

Let C ( G ) denote the number of spanning trees of a graph G . It is shown that there is a function ϵ( k ) that tends to zero as k tends to infinity such that for every connected, k ‐regular simple graph G on n vertices C ( G ) = { k [1 − δ( G )]} n . where 0 ≤ δ( G ) ≤ ϵ( k ).