We consider a path as an ordered sequence of distinct vertices with a head and a tail. Given a path, a transfer-move is to remove the tail and add a vertex at the head. A graph is n-transferable if any path with length n can be transformed into any other such path by a sequence of transfer-moves. We show that, unless it is complete or a cycle, a connected graph is δ-transferable, where δ ≥ 2 is the minimum degree. © 2008 Elsevier B.V. All rights reserved.
Torii, R. (2009). Path transferability of graphs with bounded minimum degree. Discrete Mathematics, 309(8), 2392–2397. https://doi.org/10.1016/j.disc.2008.05.015