The structure of transform graphs (Q1377873)

If \(G\) is a graph and \(v\) is a vertex of \(G\), then the transform graph \(T(G,v)\) is the graph whose vertices are the Hamiltonian paths starting at \(v\) such that two paths are neighbors if one can be obtained from the other by first deleting an edge in the path and then adding an appropriate edge. This paper contains upper bounds on the number of edges of \(T(G,v)\) for certain classes of graphs \(G\).