Regular Article
The Connectivities of Leaf Graphs of 2-Connected Graphs

https://doi.org/10.1006/jctb.1998.1895Get rights and content
Under an Elsevier user license
open archive

Abstract

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 uV, tu 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.

Cited by (0)