Vertex-Transitive Cubic Graphs of Square-Free Order


  • This work was partially supported by two Natural Science Funds of China, a Tianyuan Youth Fund of China, a Yunnan High-End-Talant-Plan fund, and an ARC Discovery Project grant of Australia.


A classification of connected vertex-transitive cubic graphs of square-free order is provided. It is shown that such graphs are well-characterized metacirculants (including dihedrants, generalized Petersen graphs, Möbius bands), or Tutte's 8-cage, or graphs arisen from simple groups PSL(2, p).