The Connectivities of Leaf Graphs of 2-Connected Graphs

Given a connected graph G, denote by V the family of all the spanning trees of G. Define an adjacency relation in V as follows: the spanning trees t and t′ are said to be adjacent if for some vertex u∈V, t−u is connected and coincides with t′−u. The resultant graph G is called the leaf graph of G. The purpose of this paper is to show that if G is 2-connected with minimal degree δ, then G is (2δ−2)-connected.