On the tree graph of a connected graph
Ana Paulina Figueroa, Eduardo Rivera‐Campo · Discussiones Mathematicae Graph Theory · 2008
Let G be a graph and C be a set of cycles of G.The tree graph of G defined by C, is the graph T (G, C) that has one vertex for each spanning tree of G, in which two trees T and T are adjacent if their symmetric difference consists of two edges and the unique cycle contained in T ∪ T is an element of C. We give a necessary and sufficient condition for this graph to be connected for the case where every edge of G belongs to at most two cycles in C.